Question

A projectile is launched from ground level to the top of a cliff which is 195 m away and 155 m high (see the figure(Figure 1)).

Part A If the projectile lands on top of the cliff 5.4 s after it is fired, find the initial velocity of the projectile (magnitude and direction). Neglect air resistance. Express your answer using two significant figures. Part B Express your answer using two significant figures.

Answer 1

Consider the initial velocity as v and the angle of projection as
The horizontal distance, x = v cos x t
195 = v cos x 5.4
v cos = 36.11 ...(1)

The vertical distance, y = vt sin - 1/2 gt²
155 = v x 5.4 x sin - 0.5 x 9.81 x (5.4)²
5.4 v sin = 298.0298
v sin = 55.19 ...(2)

(2)/(1) gives
tan = 1.528
= tan^-1(1.528)
= 56.80

Substituting in (1),
v = 36.11/cos(56.80)
= 65.95 m/s

= 57 and v = 66 in two significant figures.