201405 T3 Students Copy 1

UNIVERSITI TUNKU ABDUL RAHMAN Centre
Course
Year/ Trimester
Session
: Centre for Foundation Studies (CFS)
: Foundation in Science
: Year 1 / Trimester 1
: 201405
Unit Code
Unit Title

: FHSC1014
: Mechanics

Tutorial 3: Projectile motion and Laws of motion.

1. A boy throws a ball vertically upwards, the ball traveled 5.00 m before drop back to ground. What is the velocity of the ball when it is at 8.00 m below the initial position? [-16.0 m/s]

2. Suppose a car manufacturer tested its cars for front-end collisions by hauling them up on a crane and dropping them from a certain height. (a) Show that the speed just before a car hits the ground, after falling from rest a vertical distance H, is given by . What height corresponds to a collision at (b) 60 km/h? (c) 100km/h? [14 m, 39 m]

3. A student throws a water balloon vertically downward from the top of a building. The balloon leaves the thrower's hand with a speed of 6.00 m/s. Air resistance may be ignored, so the water balloon is in free fall after it leaves the thrower's hand. (a) What is its speed after falling for 2.00 s? (b) How far does it fall in 2.00 s? (c) What is the magnitude of its velocity after falling 10.0 m? (d) Sketch ay-t, vy-t, and y-t graphs for the motion. [(a) 25.6 m/s, (b) 31.6 m, (c) 15.6 m/s]

4. A certain volcano on earth can eject rocks vertically to a maximum height H. (a) How high (in terms of H) would these rocks go if a volcano on Mars ejected them with the same initial velocity? The acceleration due to gravity on Mars is 3.71 m/s2, and you can neglect air resistance on both planets. (b) If the rocks are in the air for a time T on earth, for how long (in terms of T) will they be in the air on Mars? [(a) 2.64H, (b) 2.64T]

5. While standing on a bridge 25.0 m above the ground, you drop a stone from rest. When the stone has fallen 3.20 m, you throw a second stone straight down. What initial velocity must you give the second stone if they are both to reach the ground at the same instant? Take the downward direction to be the positive direction. [10.1 m/s]

6. A steel ball rolls off the edge of a table top 1.20 m above the floor. If it strikes the floor 1.60 m from the base of the table, what was its initial horizontal speed? [3.23 m/s]

7. A 2.00 m tall basketball player is standing on the floor 10.0 m from the basket, as in figure. If he shoots the ball at a 40.0° angle with the horizontal, at what initial speed must he throw the basketball so that it goes through the hoop without striking the backboard? The height of the basket is 3.05 m. [10.7 m/s]

8. A student stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of 18.0 m/s. The cliff is 50.0 m above a flat, horizontal beach as shown in figure. (a) What are the coordinates of the initial position of the stone? (b) What are the components of the initial velocity? (c) Write the equations for the x- and y-components of the velocity of the stone with time. (d) Write the equations for the position of the stone with time, using the coordinates in figure. (e) How long after being released does the stone strike the beach below the cliff? (f) With what speed and angle of impact does the stone land? [(c) vx = +18.0 m/s, vy = (-9.80 m/s2)t, (d) x = (+18.0 m/s)t, y = 50.0 m –(4.90 m/s2)t2, (e) 3.19 s, (f) 36.1 m/s at 60.1o below horizontal]

9. A brick is thrown upward from the top of a building at an angle of 25° 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?
[25 m]

10. A projectile is launched with an initial speed of 60.0 m/s at an angle of 30.0° above the horizontal. The projectile lands on a hillside 4.00 s later. Neglect air friction. (a) What is the projectile’s velocity at the highest point of its trajectory? (b) What is the straight-line distance from where the projectile was launched to where it hits its target? [(a) 52.0 m/s, (b) 212 m]

11. A rock is thrown upward from the level ground in such a way that the maximum height, H of its flight is equal to its horizontal range, R. (a) At what angle  is the rock thrown? (b) Would your answer to part (a) be different on a different planet?

12. Draw a free-body diagram for the forces exerting on the traffic light in the figure below. Find the resultant force exerted by the two cables supporting the traffic light. [84.9N upwards]

13. A 5.0-g bullet leaves the muzzle of a rifle with a speed of 320 m/s. What force (assumed constant) is exerted on the bullet while it is traveling down the 0.82-m-long barrel of the rifle? [3.1×102 N]

14. Draw a free-body diagram for the forces exerting on the block as shown in figure.

15. Two crates, A and B, sit at rest side by side on a frictionless horizontal surface. The crates have masses mA and mB. A horizontal force F is applied to crate A and the two crates move off to the right. Draw clearly labeled free-body diagrams for crate A and for crate B. Indicate which pairs of forces, if any, are third-law action-reaction pairs.

16. A chair of mass 12.0 kg is sitting on the horizontal floor; the floor is not frictionless. You push on the chair with a force F = 40.0 N that is directed at an angle of 37.0o below the horizontal and the chair slides along the floor. Draw a clearly labeled free-body diagram for the chair.