#### Question

# How far from the castle wall does the launched rock hit the ground?

King Arthur's knights use a catapult to launch a rock from their vantage point on top of the castle wall, 14 m above the moat. The rock is launched at a speed of 27 m/s and an angle of 32degrees above the horizontal.

How far from the castle wall does the launched rock hit the ground?

#### Answer

Voy = 27 sin 32 = 14.3078 m/s

Vox = 27 cos 32 = 22.8973 m/s

Time projectile is in air:

Using: Y = Yo + Voy t - (1/2)gt^2

Substituting: 0 = 14.0 + (27 sin 32) - 4.9 t^2

Solve for t using quadratic formula:

t = [14.3078 +/- sqrt(479.113)]/9.8 <--- Disregard negative root as it is meaningless

t = 3.6935 seconds

X = Vo x t - (1/2)at^2 <---- a=0

x = (27 cos 32((3.6935)

x = 84.57 m

Oct 22 at 22:40