A stone is dropped from the upper observation deck of a tower, 150 m above the g

Question

A stone is dropped from the upper observation deck of a tower, 150 m above the ground. (Assume g = 9.8 m/s^2.) (a) Find the distance (in meters) of the stone above ground level at time t. (b) How long does it take the stone to reach the ground? (Round your answer to two decimal places.) (c) With what velocity does it strike the ground? (Round your answer to one decimal place.) (d) If the stone is thrown downward with a speed of 7 m/s, how long does it take to reach the ground? (Round your answer to two decimal places.)

Explanation / Answer

Consider the base of the tower at ground level to be the origin. a(t) is 9.8 regardless of time, so... initial values a(0) = -9.8????????negative because it accelerates down v(0) = 0??????????????initially, the stone doesn't move when dropped h(0) = 700 a(t) = -9.8 integrating from 0 to t will give you v(t) = -9.8t + C????????????????????v(0) = -9.8(0) + C = 0 v(t) = -9.8t ????????????????????????????????????? ??????????????????C = 0 integrating again will give you height above the ground h(t) = -4.9t² + C??????????????????h(0) = -4.9(0²) + C = 700 h(t) = -4.9t² + 700 ?????????????????????????????????????? ?????C = 700

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