Question

A catapult launches a boulder with an upward velocity of 112 ft/s. The height of the boulder, h, in feet after t seconds is given by the function h = -16t2 + 112t + 30 How long does it take the boulder to reach its maximum height? What is the boulder’s maximum height? Round to the nearest hundredth, if necessary

Answer 1

3.5 s; 226 ft is correct.

Explanation:

Answer 2

The expression for the height is given in quadratic expression form

Ax² + Bx + C

Where A, B, and C are constant

To find the x-coordinate when the graph reaches maximum/minimum, we use the formula

x = -B ÷ 2A

We have

h = -16t² + 112t + 30
The value for A = -16, B = 112, and C = 30

Substitute these into x = -B ÷ 2A we have
t = -112 ÷ (2×-16) = 3.5

The maximum height is reached when t = 3.5 sec

The height when t = 3.5 sec is given
h = -16(3.5)² + 112(3.5) + 30 = 226 feet