Assume you drop a rock from a cliff which is 5000 feet above the ground. The dis

Question

Assume you drop a rock from a cliff which is 5000 feet above the ground. The distance in feet, y, of the rock below the cliff at the time t seconds after it was dropped is given by the equation
y=-1/2gt^2

Note: y is negative since the rock is falling.

a. How far below the cliff is the rock 6 seconds after it is dropped?

____ feet

b. How far is the rock from the bottom of the canyon 6 seconds after it is dropped?
____ feet

c.When will the rock hit the bottom? Round to the nearest tenth.

____ seconds

d. The velocity of the rock at impact (in feet/sec) can be calculated by the formula

v=gt. Use your answer in part c. to calculate the rock's impact velocity.
____ feet/second

Explanation / Answer

g = 32.2 feet per second squared

a) t = 6

So, y = 1/2 x 32.2 x 62

= 579.6 feet below the cliff

b) distance from bottom of the canyon = 5000 - 579.6

= 4420.4 feet

c) here, y = 5000

5000 = 1/2 x 32.2 x t2

t2 = 310.56

t = 17.6 seconds

d) v = gt

= 32.2x17.6

= 566.7 feet/second

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