**1) **A rifle is aimed horizontally at a target 30 m away. The bullet hits the target 1.9 cm below the aiming point.

Calculate

a) the bullet’s time of flight. [62 ms]

b) its speed as it emerges from the rifle. [480 ms^{-1}]

**2)** A skier leaves a slope at 20⁰ above the horizontal with a speed of 10 ms-1. The horizontal landing surface is 3 m below the slope.

a) At what horizontal distance from the launching point does she land? [11.3 m]

b) At what impact velocity will she land? [12.6 ms^{-1}, 41.8⁰ below the horizontal]

**3)** A small ball rolls horizontally off the edge of a tabletop that is 1.2m high. It strikes the floor at a point 1.52m horizontally away from the edge of the table. Calculate

a) The time for the ball to remain in the air. [0.50 s]

b) Speed of the ball at the instant it leaves the table. [3.04 ms^{-1}]

**4) **You throw a ball with a speed of 25.3 m s-1 at an angle of 42.0 degrees above the horizontal directly towards a wall. The wall is 21.8 m from the release point of the ball

a) How long is the ball in the air before it hits the wall? [1.16 s]

b) How far above the release point does the ball hit the wall? [13.0 m]

c) What are the horizontal and vertical components of its velocity as it hits the wall? [18.8 ms^{-1}, 5.55 ms^{-1}]

**5)** In the 1991 World Track and Field Championships in Tokyo, Mike Powell jumped 8.95 m, breaking the 23-year long jump record by a full 5 cm. Assuming that Powell’s speed on takeoff was 9.5 ms-1 (about equal to that of a sprinter) and that g is 9.80 ms-2 in Tokyo. How much less was Powell’s horizontal range than the maximum possible range (neglect the effects of air resistance) for a particle launched at the same speed of 9.5 ms-1? [0.25 m]

**6)** A home run is hit in such a way that the baseball just clears a wall 21 m high, located 130 m from the home plate. The bat hits the ball when the ball is 1m above the ground. The ball is hit at an angle of 35⁰ to the horizontal, and air resistance is negligible. Find

a) The initial speed of the ball. [41.7 ms^{-1}]

b) The time it takes the ball to reach the wall. [3.81 s]

c) The velocity of the ball when it reaches the wall. [55.6 ms^{-1}]

**7)** A rock is projected 20⁰ above the horizontal at 5 ms-1 from a cliff 50 m above ground.

Find

a) The horizontal distance from the base of the cliff that the rock lands. [15.8 m]

b) The impact velocity. [31.7 ms^{-1}]

**8) **A soccer ball is kicked from the ground with an initial speed of 19.5 ms-1 at an upward angle of 45⁰. A player 55 m away in the direction of the kick starts running to meet the ball at that instant. What must be his average speed if he is to meet the ball just before it hits the ground? Neglect air resistance. [5.78 ms^{-1}]

**9)** A ball rolls horizontally off the top of a stairway with a speed of 1.52 ms-1. The steps are 20.3 cm high and 20.3 cm wide. Which step does the ball hit first? [3rd step]

**10)** During a tennis match, a player serves the ball at 23.6 ms-1, with the centre of the ball leaving the racquet horizontally 2.37 m above the court surface. The net is 12m away and 0.90 m high. When the ball reaches the net,

a) Does the ball clear it? [yes]

b) What is the distance between the centre of the ball and the top of the net? [0.2 m]

Suppose that, instead, the ball is served as before but now it leaves the racquet at 5 degrees below the horizontal. When the ball leaves the net?

c) Does the ball clear it? [no]

d) What now is the distance between the centre of the ball and the top of the net? [0.85m]

**11)** a) A body is projected from the ground level at an angle of 50⁰ above the horizontal has an initial speed of 40 ms-1. How long will it be before it hits the ground? [61.8 s]

b) A body is projected at an angle of 30⁰ below the horizontal from the top of a building 170 m high. Its initial speed is 40 ms-1. How long will it take before striking the ground? What is the velocity of the body just before it touches the ground? [4.19 s, 61.3 ms^{-1}]

**12)** a) A football is kicked at a speed of 20 m s-1 at a launch angle of 45⁰. Find its range assuming negligible air resistance. [40.8 m]

b) A stunt driver leaves a ramp at an angle of 30⁰ and lands at the same height after travelling a horizontal distance of 36 m. What was his take-off speed? [20.2 ms^{-1}]