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BlackZzzverrR [31]
3 years ago
8

two coconuts fall freely from rest at the same time, one twice as high as the other. If The coconut from the shorter tree takes

2.0 s to reach the ground, how long will it take the other coconut to reach the ground?
Physics
1 answer:
NikAS [45]3 years ago
8 0

Take the first coconut's starting position to be the origin, and the downward direction to be positive. The first coconut's position is determined by

y_1=\dfrac12gt^2

where g is the acceleration due to gravity.

So if it takes 2.0 s to reach the ground, then

y_1=\dfrac12\left(9.8\,\dfrac{\mathrm m}{\mathrm s^2}\right)(2.0\,\mathrm s)^2=20.\,\mathrm m

(rounding to 2 significant digits)

The second coconut starts 20 m higher than the first, so its initial displacement is -20 m relative to the origin, and its overall position over time is given by

y_2=-20.\,\mathrm m+\dfrac12gt^2

Reaching the ground is a matter of obtaining y_2=20\,\mathrm m, which requires a time of

20\,\mathrm m=-20\,\mathrm m+\dfrac12\left(9.8\,\dfrac{\mathrm m}{\mathrm s^2}\right)t^2\implies t=2.9\,\mathrm s

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