Key: *** = my answer
8. A catapult launches a boulder with an upward velocity of 148 ft/s. The height of the boulder, h, in feet after t seconds is given by the function h = –16t2 + 148t + 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. Reaches a maximum height of 30 feet in 9.25 seconds.
b. Reaches a maximum height of 640.5 feet in 4.63 seconds.
c. Reaches a maximum height of 1,056.75 feet in 4.63 seconds.
d. Reaches a maximum height of 372.25 feet in 4.63 seconds.
3 answers
I think its C.
dh/dt = -32t + 148
= 0 for a max of h
32t = 148
t = 148/32 = 4.625
when t = 4.625
h = -16(4.625)^2 + 148(4.625) + 3 0 = 372.25
looks like d
= 0 for a max of h
32t = 148
t = 148/32 = 4.625
when t = 4.625
h = -16(4.625)^2 + 148(4.625) + 3 0 = 372.25
looks like d
look for vertex of the parabola in algebra. (You would be able to do it much faster with calculus or physics)
t^2 - 9.25 t - 1.875 = -h/16
t^2 - 9.25 t = -h/16 + 1.875
t^2-9.25t+4.265^2 = -h/16 +1.875+21.39
( t-4.265)^2 = -1/16( h - 372.25)
So, I think it is d and at 4.265 seconds
t^2 - 9.25 t - 1.875 = -h/16
t^2 - 9.25 t = -h/16 + 1.875
t^2-9.25t+4.265^2 = -h/16 +1.875+21.39
( t-4.265)^2 = -1/16( h - 372.25)
So, I think it is d and at 4.265 seconds
46 answers