The function y = -16^2 + 486 models the height y in feet of a stone t seconds after it is dropped from the edge of a vertical cliff. How long will it take to hit the ground? Round to the nearest hundredth of a second.

A.) 7.79 seconds
B.) 0.25 seconds
C.) 5.51 seconds
D.) 11.02

The function is [tex]y=f(t)=-16t^2+486[/tex]

for example, at time t=2s , the height y of the stone is found as follows:

[tex]y=f(2)=-16\cdot 2^2+486=-16\cdot4+486=-64+486=422 (ft)[/tex]

When the ball hits the ground, the height y, becomes 0.

So we solve:

[tex]0=-16t^2+486\\\\16t^2=486\\\\t^2=\displaystyle{\frac{486}{16}=30.375[/tex]

[tex]t=\sqrt{30.375}\approx5.51[/tex]

Answer: C. 5.51 seconds

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The function y = -16^2 + 486 models the height y in feet of a stone t seconds after it is dropped from the edge of a vertical cliff. How long will it take to hit the ground? Round to the nearest hundredth of a second. A.) 7.79 seconds B.) 0.25 seconds C.) 5.51 seconds D.) 11.02

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The function y = -16^2 + 486 models the height y in feet of a stone t seconds after it is dropped from the edge of a vertical cliff. How long will it take to hit the ground? Round to the nearest hundredth of a second.

A.) 7.79 seconds
B.) 0.25 seconds
C.) 5.51 seconds
D.) 11.02