A ball is thrown into the air with an upward velocity of 36 ft/s. Its height h in feet after t seconds is given by the function

Question

1 year ago

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A ball is thrown into the air with an upward velocity of 36 ft/s. Its height h in feet after t seconds is given by the function

h = −16t2 + 36t + 10. In how many seconds does the ball reach its maximum height? Round to the nearest hundredth if necessary. What is the ball’s maximum height?

Mathematics

1 answer:

Aloiza [94] · Answer 1 · 2023-11-15T06:23:35+03:00

The ball's maximum height is 30.25 feet.

<h3>What is quadratic equation?</h3>

A quadratic equation in math is a second-degree equation of the form ax² + bx + c = 0. Here a, b, are the coefficients, c is the constant term, and x is the variable.

Given:

h= -16t²+36t+10

Differentiate w.r.t. 't',

h' = -32t+36

When h=0, that will be the maximum height

32t= 36

t= 9/8

t= 1.125 sec.

So, The maximum height is

h(1.123)= -16(1.125)² + 36*1.125+10

h(1.125) = 30.25 feet.

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