Question

A catapult launches a boulder with an upward velocity of 144 ft/s. The height of the boulder, h, in feet after t seconds is given by the function h
= -16t2 + 144t + 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

\[h(t) = -16t^2+144t+30\]

Your objective is to find the maximum value of \(h(t)\) and determine the value of \(t\) at which \(h(t)\) is maximized.

This equation is that of a parabola which opens downward (coefficient of the squared term is negative). Therefore, the vertex of the parabola is the point of maximum height, and the x-coordinate of the vertex is the time of maximum height. Do you know how to find the vertex of the parabola from the equation?

Answer 2

https://mathway.com/

Answer 3

use the site