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= -16t^2+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.

A. 7 s; 30 ft

B. 3.5 s; 366 ft

C. 3.5 s; 618 ft

D. 3.5 s; 226 ft

A, B, C, or D? Please explain :)

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= -16t^2+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.

A. 7 s; 30 ft

B. 3.5 s; 366 ft

C. 3.5 s; 618 ft

D. 3.5 s; 226 ft

A, B, C, or D? Please explain :)

campbell_st · Answer

there are 2 options to solve this problem. 

1. using calculus find the 1st derivative  with is the velocity equation. 

    the the 1st derivative = 0 and solve for t.... this give the time of the maximum height. 

    Substitute it into h(t) to find the maximum height. 

2. Find the line of symmetry, this will give the time when the maximum height occurs

use 

$$t = \frac{-b}{2a}$$        a = -16 and b = 112


when you have the value for t, substitute it into h(t) to find the maximum height.