A tutorial sheet of harder questions on projectiles is given below. Unless otherwise indicated, neglect air resistance and take g = 9.8 ms -2 .
- A ball is thrown at 65 m/s at 32° to the horizontal. At what height does it strike a vertical wall 53 m from the point of projection? [28.6m]
- A stone is projected at 24 m/s and strikes a wall 37 m from the point of projection at a height of 15 m above the level of projection. What are the angles of projection to the horizontal? [47.8°,64.3°]
- A stone is thrown at 47 m/s at 35° above the horizontal from the edge of a cliff. The stone strikes the sea at an angle of 14° below the horizontal. What is the height of the cliff? [32.4m]
- A projectile is thrown at 13° below the horizontal from the edge of a cliff. It hits the sea at 135 m/s at an angle of 23° below the horizontal. What is the speed of projection? [127.5m/s]
- A projectile is thrown from a cliff and strikes the sea 56 m from the foot of the cliff at 97 m/s at 49° below the horizontal. What is the speed of projection? [90.7m/s]
- If a projectile strikes the sea at 140 m/s at 35° below the horizontal after being in flight for 12.0 s, what is the angle at which it was projected? [+18.0°]
- A projectile strikes the sea 65.0 m from the base of a cliff of height 127 m after being projected at 92.0 m/s. What is the angle of projection to the horizontal? [-60.9°]
- When a projectile lands below its initial level the maximum horizontal range is obtained at an angle of projection less than 45°. In shotput the shot leaves the hand at a height h above the ground at a speed u. Show that the angle of projection above the horizontal for maximum range is given by tan𝜽=1/(√(1+2gh/v2)).
- A projectile is thrown at an angle of 45° to the horizontal. Sketch, on the same axes, the path of the projectile when (i) air resistance is neglected, (ii) air resistance is included.