Question

Britney throws an object straight up into the air with an initial velocity of 27 ft/s from a platform that is 10 ft above the ground. Use the formula h(t)=−16t2+v0t+h0 , where v0 is the initial velocity and h0 is the initial height. How long will it take for the object to hit the ground?

1s

2s

3s

4s

Answer 1

h(t) = -16t^2 + 27x + 10
At the point the object hits the ground, h(x) = 0
-16x^2 + 27x + 10 = 0
16x^2 - 27x - 10 = 0
x = (27 + sqrt(27^2 - 4 x 16 x -10)) / (2 x 16) = (27 + sqrt(729 + 640)) / 32 = (27 + 37) / 32 = 64 / 32 = 2

Therefore, the object will hit the ground after 2 seconds.

Answer 2

The time it took the object to reach the ground to be 2 secs

Equation of the height of an object

Given the equation that represents the height of an object as h(t)=−16t2+v0t+h0.

If the initial velocity of 27 ft/s from a platform that is 10 ft above the ground, then;

h(t) = -16t^2 + 27x + 10

At the point the object hits the ground, h(x) = 0

-16x^2 + 27x + 10 = 0

16x^2 - 27x - 10 = 0

Factorizing the result will give the time it took the object to reach the ground to be 2 secs

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