Question

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.

Answer 1

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