Question

King Arthur's knights use a catapult to launch a rock from their vantage point on top of the castle wall, 13 m above the moat. The rock is launched at a speed of 30 m/s and an angle of 38 ∘ above the horizontal. How far from the castle wall does the launched rock hit the ground?

Answer 1

Find the initial velocity components

Initial vertical velocity:-

Uv = 30*sin38

Uv = 18.47 m/s

Initial horizontalvelocity

Uh = 30*cos38

Uh = 23.64 m/s

Find time of flight by applying d = Uv*t - 1/2gt^2 to the vertical motion

(taking ↑ as +, net displacement d = - 13m, a = - 9.80 m/s^2)

- 13 = (18.47t) - (1/2 x 9.80 x t^2)

4.90t^2 - 18.47t - 13 = 0

a quadratic equation to solve to find t

t = 4.3757 sec

Horizontal distance = Vh x time of flight (t)

Dh = 18.47 m/s x 4.3757 s

Dh = 80.82 m