Math CentralQuandaries & Queries


Question from Michelle, a student:

A crate is launched from an airplane, 75 feet above the ocean, with an initial vertical velocity of 60 feet per second. How many seconds will it take for the crate to hit the water? Round to the nearest hundredth.

(Hint: Use the vertical motion model for earth: h=16t^2+vt+s, where h is the height of the object (in feet) at any time t seconds after release, v is the initial velocity of the object in feet/second, and s is the initial height of the object (in feet) before being released.

What I did:

To solve this problem, I first set h equal to 0, since the crate will reach the water when the height is 0 seconds. v=60 feet and s=75 feet. After plugging the numbers into the equation, I did not understand what to do next. Please help me step by step. Thanks.

Hi Michelle,

In the expression h=16t2+vt+s the number 16 is a/2 where a is the acceleration due to gravity. a = 32 feet/sec2. The force of gravity is acting downwards on the crate and hence the vertical distance is measured downwards. Thus if you make s = 0 feet then when the crate hits the ground h = 75 feet. Substituting into the expression then gives

75 = 16t2 + 60t + 0


16t2 + 60t - 75 = 0

The next step is to solve for t.

If you need more assistance write back.


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