Question

HELPA catapult launches a boulder with an upward velocity of 122 feet per second. The height of the boulder H in feet in after T seconds is given by the function H(t)= -16t^2 + 122t + 10. what is the boulders maximum height. how long does it take the boulder to reach it's maximum height

Answer 1

The height of the boulder H in feet in after T seconds is given by the function H(t)= -16t^2 + 122t + 10. what is the boulders maximum height. how long does it take the boulder to reach it's maximum height

Answer 2

The boulder's maximum height is 242.6 feet.

It takes the boulder 3.79 seconds to reach its maximum height

What is Motion?

From the question, we are to determine the maximum height of the boulder

First, we will calculate the time it took the boulder to reach its maximum height

Using the formula,

v = u - gt

Where v is the final velocity

u is the initial velocity

g is the acceleration due to gravity (g = 32.1741 ft/s²)

and t is the time

From the given information

u = 122 ft/s

At maximum height, v = 0 ft/s

Putting the parameters into the equation, we get

0 = 122 - 32.1741t

32.1741t = 122

t = 3.79 s

This means it takes the boulder 3.79 seconds to reach its maximum height.

Now, substitute the value of t into the function that gives the height of the boulder

From the given information,

The height of the boulder is given by

H(t)= -16t² + 122t + 10

Then,

H(3.79) = -16(3.79)² + 122(3.79) + 10

H(3.79) = -229.8256 + 462.38 + 10

H(3.79) = 242.5544

H(3.79) ≅ 242.6 ft

Hence, the boulder's maximum height is 242.6 feet.

It takes the boulder 3.79 seconds to reach its maximum height

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