Physics homework. Please help with both parts. Thank you A rock is tossed straig

Question

Physics homework. Please help with both parts. Thank you

A rock is tossed straight up with a speed of 24 m/s. When it returns, it falls into a hole 10 m deep. In other words, assume that the rock lands 10 m lower than the height from which it was thrown. Take "up" to be the positive direction for this problem. Although the numbers in this problem have less than 3 significant figures, please enter your answers with at least 3 significant figures, and remember that velocity is a vector. What is the rock's velocity as it hits the bottom of the hole? m/s How long is the rock in the air, from the instant it is released until it hits the bottom of the hole? s

Explanation / Answer

Define the positive direction as the direction pointing upward and s = 0 when t = 0. Denote the time it takes for the rock to hit the bottom of the hole as t.

We have

-10 = - 0.5 g t^2 + 24

4.9t^2 - 24t - 10 = 0

solutions are t = 5.284 sec

The velocity when the rock hits the bottom of the hole is

v(5.284) = - 9.8 * 5.284 + 24 = -27.783 m/sec

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