Question

Benjamin threw a rock straight up from a cliff that was 40 ft above the water. If the height of the rock h, in feet, after t

seconds is given by the equation h = - 16t* + 12t + 40, how long will it take for the rock CO hit the water?

Answer 1

Explanation:

To find the time it takes for the rock to hit the water, we need to find the value of t when h is equal to zero. This is because the rock will hit the water when it reaches a height of zero feet above the water.

Substituting zero for h in the equation h = -16t^2 + 12t + 40, we get:

0 = -16t^2 + 12t + 40

This equation is a quadratic in t, so we can use the quadratic formula to solve for t:

t = (-12 +/- sqrt(12^2 - 4 * (-16) * 40)) / (-32)

Simplifying, we get:

t = (-12 +/- sqrt(144 + 640)) / (-32)

t = (-12 +/- sqrt(784)) / (-32)

t = (-12 +/- 28) / (-32)

t = -40/-32 or t = 16/-32

t = 1/8 or t = -1/2

Since the time cannot be negative (because the rock was thrown upwards), the only solution that makes sense is t = 1/8 seconds.

Therefore, it will take 1/8 seconds for the rock to hit the water.