Kinematics

1. A car traveling at a constant speed of 30 m/s passes a police car at rest. The policeman starts to move at the moment the speeder passes his car and accelerates at a constant rate of 3.0 m/s2 until he pulls even with the speeding care. Find a) the time required for the policeman to catch the speeder and b) the distance traveled during the chase.

2. A tennis ball with a velocity of 10.0 m/s is thrown perpendicularly at a wall. After striking the wall, the ball rebounds in the opposite direction with a velocity of 8.0 m/s. If the ball is in contact with the wall for 0.012 s, what is the average acceleration of the ball while it is in contact with the wall?

3. In Mostar, Bosnia, the ultimate test of a young man's courage was to jump off a 400 year old bridge (now destroyed) into the River Neretva, 23 m below the bridge. (a) How long did the jump last? (b) How fast was the diver traveling upon impact with the water?

4. 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 negative acceleration of -2.0 m/s2. If the brakes are applied for 3.0 s, how fast is the car going to at the end of the braking period, and how far has it gone from the start?

5. A dog searching for a bone walks 3.50 m south (270° from +x axis), then 8.20 m at an angle of 30.0o north of east (30o from +x axis) and finally 15.0m west (180° from + axis). What is the magnitude and direction of the dog's resultant displacement?

6. 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 15.0 m/s. If the brick is in flight for 3.0 s, how tall is the building?

7. Lex Luthor, Superman's enemy, drops a vial of Kyrptonite from the edge of a 50.0m tall building. Superman, who is walking towards the building at a velocity of 5.0 m/s, sees the vial being dropped. If Superman can accelerate at 25.0 m/s2, what is the maximum distance that he can be from the building and manage to catch the vial before it contacts the ground? Superman's reaction time is instantaneous.

8. A projectile is fired with an initial speed of 113 m/s at an angle of 60° above the horizontal from the top of a 49 m high cliff. Find a) the time to reach the maximum height, b) the maximum height, c) the total time in the air, d) the horizontal range and e) the components of the final velocity just before the projectile hits the ground.