13. A catapult launches a boulder wint an upward velocity of 122 feet per second the height of the boulder (h) in feet after t seconds is given by the function h(t)=-16t^2+122t+10. How long does it take the boulder to reach maximum height? What is the boulders maximum height? Round to the nearest hundredth if necessary.
Accepted Solution
A:
For this case we have the following expression: h (t) = - 16t ^ 2 + 122t + 10 We look for the maximum of the function, for this, we derive: h '(t) = - 32t + 122 We match zero: -32t + 122 = 0 We cleared t: t = 122/32 t = 3.8125 s Then, the maximum height will be: h (3.8125) = - 16 * (3.2185) ^ 2 + 122 * (3.2185) +10 h (3.8125) = 236.92 feet Answer: It takes the boulder to reach maximum height about: t = 3.8125 s the boulders maximum height is: 236.92 feet