A catapult launches a boulder with an upward velocity of 92 m/s. The height of the boulder, h, in meters after t seconds is given by the function h = –5t2+ 92t + 16. How long does it take to reach maximum height? What is the boulder’s maximum height? Round to the nearest hundredth, if necessary. (1 point)

Question

A catapult launches a boulder with an upward velocity of 92 m/s. The height of the boulder, h, in meters after t seconds is given by the function h = –5t2+ 92t + 16. How long does it take to reach maximum height? What is the boulder’s maximum height? Round to the nearest hundredth, if necessary.  (1 point)
 Reaches a maximum height of 16.00 meters in 18.4 seconds.
 Reaches a maximum height of 18.57 meters in 9.2 seconds. MY ANS.
 Reaches a maximum height of 37.14 meters in 18.4 seconds.
 Reaches a maximum height of 439.20 meters in 9.2 seconds.

Anonymous · Accepted Answer

Wrong.

Given a quadratic equation, the x-value that will always yield the maximum y-value is given by the equation:

x = -b/2a

So, in this case...
t = -(92)/2(-5) = 9.2 sec

Therefore, the boulder will reach it's maximum height at 9.2 sec. Now, just plug n' chug it into the function...

h = -5(9.2)² + 92(9.2) + 16
h = 439.20 m

You can also make a logical assumption. Think about it: you are launching a boulder 92 m/s in the air...the max height is bound to be great.

Kat · Answer

Thanks that really helped <3

sydney · Answer

thanksssss so much

annoymous · Answer

So it’s d?

Trebuchet · Answer

However, the catapult cannot really launch a 90 kilogram object over 300 meters.

i g0T u Br0 ^-^ · Answer

correct answer should be : D. Reaches a maximum height of 439.20 meters in 9.2 seconds.

NaruUzi · Answer

thx

Bot · Answer

You're welcome! Don't hesitate to ask if you have any more questions.