# physics

a man stands on the roof of a 15.0m tall building and throws a rock with a velocity of magnitude 30.0m/s at an angle of 33 degrees above the horizontal. ignoring resistance calculate the horizontal distance from the base of the building to the point where the rock strikes the ground.

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1. Given
v=30 m/s
θ=33°
h=15m
g=9.8 m/s²

Resolve velocity into horizontal (vx) ad vertical (vy) components,
vy=v*sin(θ)= 16.34 m/s
vx=v*cos(θ)= 25.16 m/s

Find time t to reach ground h m below:
y=vy*t+(1/2)at²
-15=16.34t-4.9t²
=>
4.9t²-16.34t-15=0
t=4.084 s (reject negative root)

Calculate horizontal distance
x=vx*t
= 25.16*4.084
= 102.8 m (approx.)

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