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sweet [91]
3 years ago
8

After a baseball is hit, the height h (in feet) of the ball above the ground t seconds after it is hit can be approximated by th

e equation h = -16t² + 64t + 3. Determine how long it will take for the ball to hit the ground. Round your answer to the nearest hundredth... Please help .. It is due tomorrow
Mathematics
1 answer:
lubasha [3.4K]3 years ago
4 0

Answer:

The ball will take 4.05 seconds to hit the ground.

Step-by-step explanation:

we have

h=-16t^{2}+64t+3

This is a quadratic equation (vertical parabola) open down

The vertex is a maximum

we know that

The ball hit the ground when h=0

Solve the quadratic equation

For h=0

-16t^{2}+64t+3=0

The formula to solve a quadratic equation of the form

at^{2} +bt+c=0 is equal to

t=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}

in this problem we have

-16t^{2}+64t+3=0  

so

a=-16\\b=64\\c=3

substitute in the formula  

t=\frac{-64(+/-)\sqrt{64^{2}-4(-16)(3)}} {2(-16)}

t=\frac{-64(+/-)\sqrt{4,288}} {-32}

t=\frac{64(-)\sqrt{4,288}} {32}=-0.05\ sec  ---> the time cannot be a negative number

t=\frac{64(+)\sqrt{4,288}} {32}=4.05\ sec

therefore

The ball will take 4.05 seconds to hit the ground.

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