UTA

An object is thrown downward with an initial
speed of 10 m/s from a height of 49 m above
the ground. At the same instant, a second
object is propelled vertically up from ground
level with a speed of 29 m/s .
At what height above the ground will the
two objects pass each other? The acceleration
of gravity is 9.8 m/s
2
.
Answer in units of m

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  1. First solve for the time when they are at the same height.

    49 - 10 t - 4.9 t^2 = 29 t - 4.9 t^2

    The t^2 terms cancel.
    39t = 49
    t = 1.2564 seconds

    Then, use the height vs. time equation for either object for the vertical height at that time.

    Y = 29t - 4.9 t^2 = 28.7 meters

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