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hram777 [196]
3 years ago
12

Benjamin threw a rock straight up from a cliff that was 48 ft above the water. If the height of the rock​ h, in​ feet, after t s

econds is given by the equation h = -16 t² + 52 t + 48, how long will it take for the rock to hit the​ water?
Mathematics
1 answer:
fomenos3 years ago
5 0

Answer: It will take 4 seconds  for the rock to hit the​ water.

Step-by-step explanation:

Given : Benjamin threw a rock straight up from a cliff that was 48 ft above the water.

If the height of the rock​ h, in​ feet, after t seconds is given by the equation

h = -16 t^2+ 52 t + 48

To find : Time taken for the rock to hit the​ water.

When rock hit the water height becomes zero , i.e. put h = 0 , we get

-16 t^2+ 52 t + 48 =0

Divide equation by 2 , we get

-8t^2+26t+24=0

The Laue of x for ax²+bx+c =0 is x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}

So , t=\frac{-26\pm\sqrt{(26^{2}-4(-8)(24))}}{2(-8)}

t=\dfrac{-26\pm 38}{-16}\\\\ t=-\dfrac{-26+38}{-16}=-0.75\ \ t=\dfrac{-26-38}{-16}=4

Since t cannot be negative , so t= 4

Hence, it will take 4 seconds  for the rock to hit the​ water.

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