Acad. Year 011-2012 Subject Physics Variant id number

A new circus act is called the Texas Tumblers. Lovely Mary Belle swings from a trapeze, projects herself at an angle of 53⁰, and is supposed to be caught by Joe Bob, whose hands are 6.1 m above and 8.2 m horizontally from her launch point (Fig. 1). You can ignore air resistance. (a) What initial speed v₀ must Mary Belle have just to reach Joe Bob? (b) For the initial speed calculated in part (a), what are the magnitude and direction of her velocity when Mary Belle reaches Joe Bob? (c) Assuming that Mary Belle has the initial speed calculated in part (a), draw x-t, y-t, v_x-t, and v_y-t graphs showing the motion of both tumblers. Your graphs should show the motion up until the point where Mary Belle reaches Joe Bob. (d) The night of their debut performance, Joe Bob misses her completely as she flies past. How far horizontally does Mary Belle travel, from her initial launch point, before landing in the safety net 8.6 m below her starting point?

A speedboat increases its speed uniformly from 20m/s to 30m/s in a distance of 200m. Find (a) the magnitude of its acceleration and (b) the time it takes the boat to travel the 200-m distance.

A body is thrown with the velocity v₀ at angle to the horizon. The duration of motion 2.2 seconds. Find the maximum height reached by the body

1. 
   A man pushing a mop across a floor causes the mop to undergo two displacements. The first has a magnitude of 150cm and makes an angle of 120 with the positive x-axis. The resultant displacement has a magnitude of 140cm and is directed at an angle of 35.0 to the positive x-axis. Find the magnitude and direction of the second displacement.
   
2. 
   

   Fig.1

   Two trains are initially moving at 5.00 m/s and at 7.00 m/s on parallel tracks with train1 50.0 m ahead of train 2. Both trains accelerate simultaneously, train 1 at the rate of 2.00 m/s² and train 2 at the rate of 2.50 m/s². How long will it take train 2 to overtake train 1? How far will train 2 travel before it overtakes train 1?
   
3. 
   A man is riding on a flatcar traveling at a constant speed of 9.10 m/s (Fig. 1). He wishes to throw a ball through a stationary hoop 4.90 m above the height of his hands in such a manner that the ball will move horizontally as it passes through the hoop. He throws the ball with a speed of 10.8 m/s with respect to himself. (a) What must the vertical component of the initial velocity of the ball be? (b) How many seconds after he releases the ball will it pass through the hoop? (c) At what horizontal distance in front of the hoop must he release the ball? (d) When the ball leaves the man's hands, what is the direction of its velocity relative to the frame of reference of the flatcar? Relative to the frame of reference of an observer standing on the ground
   
4. 
   A uniformly accelerating train passes a green light signal at 25.0 km/hr. It passes a second light 125 m farther down the track, 12.0 s later. What is the train's acceleration? What is the train's velocity at the second light
   
5. 
   A brick is thrown upward from the top of a building at an angle of 25⁰ to the horizontal and with an initial speed of 15 m/s. If the brick is in flight for 3.0 s, how tall is the building
   

1. 
   

   Fig.1

   The relationship between the distance s traveled by a body and the time t is described by the equation s =A + Bt + Ct², where A = 3 m, B = 2 m/s and C = 1 m/s². Determine the average velocity and the average acceleration of the body during the first, second and third seconds of motion.
   
2. 
   The figure 1 shows the paths of tennis ball your friend drops from the window of her apartment and of the rock you throw from the ground at the same instant. The rock and the ball collide at x = 50.0 m, y = 10.0 m and t = 3.00 s. If the ball was dropped from a height of 54.0 m, determine the velocity of the rock initially and at the time of its collision with the ball.
   
3. 
   A bus travels 500 m between two stops. It starts from rest at an acceleration of 2 m/s² until reaches a speed of 12 m/s. The bus continues at this speed and then decelerates at 3 m/s² until it comes to the stop. Find the total time required for the trip
   

4. 
   A river flows due south with a speed of 2.0 m/s. A man steers a motorboat across the river; his velocity relative to the water is 4.2 m/s due east. The river is 800 m wide. (a) What is his velocity (magnitude and direction) relative to the earth? (b) How much time is required to cross the river? (c) How far south of his starting point will he reach the opposite bank?
   
5. 
   A car moving at a velocity of 6 m/s is followed by another car which has a velocity of 30 m/s. When the first car approaches 200 m to the other car, it applies brakes and decelerates at a constant acceleration of 1 m/s². Do these two cars collide with each other? If so, when and where
   

1. 
   

   N mg F m1g m2g

   Figure2

   Fig.1

   The position of an object as a function of time is given as x = At³ + Bt² + Ct + D. The constants are A = 2.1 m/s³,B = 1.0 m/s², C = –4.1 m/s, and D = 3 m. a) What is the velocity of the object at t = 10.0 s? b) At what time(s) is the object at rest? c) What is the acceleration of the object at t = 0.50 s? d) Plot the acceleration as a function of time for the time interval from t = –10.0 s to t = 10.0 s.
   
2. 
   You drop a water balloon straight down from your dormitory window 80.0 m above your physics professor’s head. At 2.00 s after you drop the balloon, not realizing it has water in it your professor fires a dart from a gun, which is at the same height as his head, directly upward toward the balloon with an initial velocity of 20.0 m/s. a) how long after you drop the balloon will the dart burst the balloon? b) How long after the dart hits the balloon will your professor have to move out of the way of the falling water? Assume the balloon breaks instantaneously at the touch of the dart.
   
3. 
   A physics professor did daredevil stunts in his spare time. His last stunt was an attempt to jump across a river on a motorcycle (Fig.1). The takeoff ramp was inclined at 53⁰, the river was 40.0 m wide, and the far bank was 15.0 m lower than the top of the ramp. The river itself was 100 m below the ramp. You can ignore air resistance. (a) What should his speed have been at the top of the ramp to have just made it to the edge of the far bank? (b) If his speed was only half the value found in (a), where did he land?
   
4. 
   Two objects with masses of 100 g each are connected by a light string that passes over a frictionless pulley, as in Figure 2. An overload with mass of 10 g is placed on one of the weights. Determine the force which overload acts on the weight and also force of pressure acting on the block axis.
   
5. 
   A large ice block of mass M = 80.0 kg is held stationary on a frictionless ramp. The ramp is at an angle of α = 36.9° above the horizontal. a) If the ice block is held in place by a tangential force along the surface of the ramp (at angle α above the horizontal), find the magnitude of this force. b) If, instead, the ice block is held in place by a horizontal force, directed horizontally toward the center of the ice block, find the magnitude of this force.
   

1. 
   

   Figure 1

   Figure 2

   Fig. 3

   A man pushing a mop across a floor causes the mop to undergo two displacements. The first has a magnitude of 150cm and makes an angle of 120⁰ with the positive x-axis. The resultant displacement has a magnitude of 140cm and is directed at an angle of 35⁰ to the positive x-axis. Find the magnitude and direction of the second displacement
   

2. 
   A ball is thrown straight upward in the air at a speed of 15.0 m/s. Ignore air resistance. a) What is the maximum height the ball will reach? b) What is the speed of the ball when it reaches 5.00 m? c) How long will it take to reach 5.00 m above its initial position on the way up? d) How long will it take to reach 5.00 m above its initial position on its way down?
   

3. 
   A stone is thrown upward from the top of a building at an angle of 30.0⁰ to the horizontal and with an initial speed of 20.0 m/s, as in Figure 1. The point of release is 45.0 m above the ground. (a) How long does it take for the stone to hit the ground? (b) Find the stone’s speed at impact. (c) Find the horizontal range of the stone
   
4. 
   A man weighs a fish with a spring scale attached to the ceiling of an elevator, as shown in Figure 2. While the elevator is at rest, he measures a weight of 40.0N. (a) What weight does the scale read if the elevator accelerates upward at 2.00m/s²? (b) What does the scale read if the elevator accelerates downward at 2.00m/s²? (c) If the elevator cable breaks, what does the scale read?
   

5. 
   Two blocks connected by a cord passing over a small, frictionless pulley rest on frictionless planes (Fig. 3). (a) Which way will the system move when the blocks are released from rest? (b) What is the acceleration of the blocks? (c) What is the tension in the cord?
   

Fig.1

Fig.2

Fig.3

Figure 4

1. 
   Three horizontal ropes pull on a large stone stuck in the ground, producing the vector forces A, B, and C shown in Fig. 1. Find the magnitude and direction of a fourth force on the stone that will make the vector sum of the four forces zero.
   

2. 
   You are on the roof of the TTPU building, 46.0 m above the ground (Figure 2). Your physics professor, who is 1.80 m tall, is walking alongside the building at a constant speed of 1.20 m/s. If you wish to drop an egg on your professor's head, where should 1.80 m the professor be when you release the egg? Assume that the egg is in free fall.
   
3. 
   A small motor boat takes 40 s to travel 120 m upstream and 20 s to travel the same distance downstream. Find the speed of the river’s current and the speed of the boat relative to the water both upstream and downstream.
   
4. 
   A mass m₁ = 20.0 kg on a frictionless ramp is attached to a light string (Fig.3). The string passes over a frictionless pulley and is attached to a hanging mass m₂. The ramp is at an angle of θ = 30.0° above the horizontal. m₁ moves up the ramp uniformly (at constant speed). Find the value of m₂.
   
5. 
   Three objects are connected by light strings as shown in Figure 4. The string connecting the 4.00-kg object and the 5.00-kg object passes over a light frictionless pulley. Determine (a) the acceleration of each object and (b) the tension in the two strings.
   

1. 
   A train starts from rest at a station and has an acceleration of 8 m/s² for 20 s. It then runs at a constant speed for 120 s and decelerates at 10 m/s² until it stops at the next station. Find the total time and distance covered.
   
2. 
   A ball is thrown upward from the ground with an initial speed of 25m/s; at the same instant, another ball is dropped from a building 15 m high. After how long will the balls be at the same height?
   
3. 
   

   Fig.1

   Fig.2

   Y ou want to cross a straight section of a river that has a uniform current of 5.33 m/s and is 127 m wide. Your motorboat has an engine that can generate a speed of 17.5 m/s for your boat. Assume that you reach top speed right away (that is, neglect the time it takes to accelerate the boat to top speed). a) If you want to go directly across the river with a 90° angle relative to the riverbank, at what angle relative to the riverbank should you point your boat? b) How long will it take to cross the river in this way? c) In which direction should you aim your boat to achieve minimum crossing time? d) What is the minimum time to cross the river? e) What is the minimum speed of your boat that will still enable you to cross the river with a 90° angle relative to the riverbank?
   
4. 
   In the diagram m_C = 0.3 kg, m_A = 2 kg, m_B = 0.5 kg. The table is frictionless. Find (a) acceleration of system and the difference of the tensions (Fig.1).
   
5. 
   In the diagram m₁ = 300 g, m₂ = 400 g. Find (a) the acceleration of the system and (b) tension in the rope (Fig.2).
   

1. 
   

   Fig.1

   Fig.2

   Fig.3

   Compute the x- and y-components of the vectors A, B, C, and D in Fig.1
   
2. 
   Car A is at rest at a stop light. Just as the light changes, car A begins with a constant acceleration of 15 m/s². At the same time, car B moving at a constant speed of 60 m/s passes the car A. (a) if they move along a straight road, how long will it take before the car A overtakes the car B? (b) How far will they have traveled when this happens? (c) What is the speed of car A at that instant?
   
3. 
   Wild geese are known for their lack of manners. One goose is flying northward at a level altitude of h_g = 30.0 m above a north-south highway, when it sees a car ahead in the distance moving in the southbound lane and decides to deliver (drop) an “egg.” The goose is flying at a speed of v_g = 15.0 m/s , and the car is moving at a speed of v_c =100.0 km/h. a) Given the details in the figure, where the separation between the goose and the front bumper of the car, d = 104.1 m, is specified at the instant when the goose takes action, will the driver have to wash the windshield after this encounter? (The center of the windshield is h_c = 1 m off the ground.) b) If the delivery is completed, what is the relative velocity of the “egg” with respect to the car at the moment of the impact (Fig.2)?
   
4. 
   Find the tension in the string between masses m₂ and m₃, if m₁ = 10 kg, m₂ = 2 kg, m₃ = 1 kg (Fig.3).
   

1. 
   

   Fig.2

   Fig.2

   A car starts from rest and travels for 5.0 s with a uniform acceleration of +1.5 m/s². The driver then applies the brakes, causing a uniform acceleration of - 2.0 m/s². If the brakes are applied for 3.0 s, (a) how fast is the car going at the end of the braking period, and (b) how far has the car gone?
   
2. 
   A small mailbag is released from a helicopter that is descending steadily at 1.50 m/s. After 2.00 s, (a) what is the speed of the mailbag, and (b) how far is it below the helicopter? (c) What are your answers to parts (a) and (b) if the helicopter is rising steadily at 1.50 m/s.
   
3. 
   A batter hits a baseball so that it leaves the bat at speed v₀ = 37 m/s at an angle α = 53.1⁰, at a location where g = 9.80 m/s². (a) Find the position of the ball, and the magnitude and direction of its velocity, at t = 2.00 s. (b) Find the time when the ball reaches the highest point of its flight and find its height h at this point. (c) Find the horizontal range R-that is, the horizontal distance from the starting point to where the ball hits the ground.
   
4. 
   In the diagram m=m=4 kg and x= 2 kg. If the surfaces are frictionless, find the magnitude of the acceleration of the system (Fig.2).
   
5. 
   Two objects with masses of 3.00 kg and 5.00 kg are connected by a light string that passes over a frictionless pulley, as in Figure 2. Determine (a) the tension in the string, (b) the acceleration of each object, and (c) the distance each object will move in the first second of motion if both objects start from rest.
   

1. 
   

   Fig.1

   Fig.2

   Two cars are traveling along a straight line in the same direction, the lead car at 25.0m/s and the other car at 30.0m/s. At the moment the cars are 40.0m apart, the lead driver applies the brakes, causing his car to have an acceleration of 2.00m/s². (a) How long does it take for the lead car to stop? (b) Assuming that the chasing car brakes at the same time as the lead car, what must be the chasing car’s minimum negative acceleration so as not to hit the lead car? (c) How long does it take for the chasing car to stop?
   
2. 
   A student throws a set of keys vertically upward to his fraternity brother, who is in a window 4.00 m above. The brother’s outstretched hand catches the keys 1.50 s later. (a) With what initial velocity were the keys thrown? (b) What was the velocity of the keys just before they were caught?
   
3. 
   A ball is thrown from a bridge 100 m high at an initial velocity of 30 m/s at an angle of 50⁰ above the horizontal. Find (a) how high the ball goes, (b) the total time the ball is in the air, (c) the maximum horizontal distance that the ball travels, and (d) the velocity of the ball as it strikes the ground.
   
4. 
   A 10 kg object is pulled by a force of 100 N as in the Fig. 1. (a) Find the acceleration of the object if there is no friction. (b) Find the distances in 5 s.
   
5. 
   Two horses are pulling a barge with mass 2.00· 10³ kg along a canal, as shown in Figure 2. The cable connected to the first horse makes an angle of 40⁰ with respect to the direction of the canal, while the cable connected to the second horse makes an angle of 20⁰. Find the initial acceleration of the barge, starting at rest, if each horse exerts a force of magnitude 6.00· 10² N on the barge. Ignore forces of resistance on the barge