Question 1a
A rock is thrown off a cliff at a height of 150 m and lands 90 m away.
(a)
(i)
Calculate the speed at which it was thrown.
[2]
(ii)
State an assumption required to obtain your answer.
[1]
Question 1b
(b)
Determine the angle at which the rock makes impact with the ground.
[2]
Question 1c
The rock is loaded into a catapult and is launched at 40° elevation from the ground toward a castle wall, with a speed of 27 m s–1. The castle wall is 50 m away and is 12 m high.
(c)
Determine whether the rock makes it over the wall.
[4]
Question 1d
(d)
Prove that the maximum range of any projectile that starts and ends at ground level is achieved when launched at an angle of elevation of 45°.
You may wish to use the double angle formula:
[4]