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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