Kylee24
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A catapult launches a boulder with an upward velocity of 120 ft/s. The height of the boulder, h,
in feet after t seconds is given by the function h=-167 + 120t + 10. How long does it take to
reach maximum height? What is the boulder's maximum height? Round to the nearest
hundredth, if necessary.
a. Reaches a maximum height of 235.00 feet in 3.75 seconds.
b. Reaches a maximum height of 10.00 feet in 7.50 seconds.
c. Reaches a maximum height of 7.58 feet in 3.75 seconds.
d. Reaches a maximum height of 15.16 feet in 7.5 seconds.

Respuesta :

Answer:

Reaches a maximum height of 235.00 feet in 3.75 seconds.

Step-by-step explanation:

The height of the boulder, h,  in feet after t seconds is given by the function is given by :

[tex]h=-16t^2+120t+10[/tex] .....(1)

For maximum height, put [tex]\dfrac{dh}{dt}=0[/tex]

i.e.

[tex]\dfrac{d(-16t^2+120t+10)}{dt}=0\\\\-32t+120=0\\\\32t=120\\\\t=3.75\ s[/tex]

Put t = 3.75 in equation (1). So,

[tex]h=-16(3.75)^2+120(3.75)+10\\\\h=235\ \text{feet}[/tex]

So, the boulder's maximum height is 235 feets and it takes 3.75 s to reach to its maximum height.

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