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17 June, 09:30

An object is dropped from rest into a pit, and accelerates due to gravity at roughly 10 m/s2. It hits the ground in 5 seconds. A rock is then dropped from rest into a second pit, and hits the ground in 10 seconds. How much deeper is the second pit, compared to the first pit?

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  1. 17 June, 12:17
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    Second pit is 375 m deeper compared to first pit.

    Explanation:

    We have equation of motion s = ut + 0.5at²

    First object hits the ground after 5 seconds,

    Initial velocity, u = 0 m/s

    Acceleration, a = 10 m/s²

    Time, t = 5 s

    Substituting,

    s = ut + 0.5 at²

    s = 0 x 5 + 0.5 x 10 x 5²

    s = 125 m

    Depth of pit 1 = 125 m

    Second object hits the ground after 10 seconds,

    Initial velocity, u = 0 m/s

    Acceleration, a = 10 m/s²

    Time, t = 10 s

    Substituting,

    s = ut + 0.5 at²

    s = 0 x 10 + 0.5 x 10 x 10²

    s = 500 m

    Depth of pit 2 = 500 m

    Difference in depths = 500 - 125 = 375 m

    Second pit is 375 m deeper compared to first pit.
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