A canyon is 900 meters deep at its deepest point. A rock is dropped from the rim above this point. Write the height of the rock as a function of time

Elleanor Mckenzie

Elleanor Mckenzie

Answered question

2021-01-31

A canyon is 900 meters deep at its deepest point. A rock is dropped from the rim above this point. Write the height of the rock as a function of time t in seconds. (Use -9.8 m/s2 as the acceleration due to gravity.) How long will it take the rock to hit the canyon floor? (Give your answer correct to 1 decimal place.)

Answer & Explanation

timbalemX

timbalemX

Skilled2021-02-01Added 108 answers

The height as a function of time h(t) is equal to the initial velocity of the rock v(0) times time (t) plus 12 the acceleration due to gravity (g) times time square (t2). That is, h(t)=v(0)×t+0.5×g×t2
Since the rock is dropped and not thrown, there is no initial velocity. Thus, v(0)=0 and h(t)=0.5×g×t2
Assuming the height at the top of the canyon is 0, when the rock hits the canyon floor, h(t)=900.

900=0.5(9.8)t2
Solving for t, 2×9009.8=t2
t=13.6seconds

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