Question

A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the maximum height reached by the rocket, . y=-16x^2+261x+130

Answer 1

The calculated maximum height reached by the rocket is 1194.39 feet

How to determine the maximum height reached by the rocket

From the question, we have the following parameters that can be used in our computation:

y = -16x² + 261x + 130

Differentiate the function and set it to 0

So, we have

-32x + 261 = 0

This gives

32x = 261

So, we have

x = 8.15625

The maximum height reached by the rocket is calculated as

Max height = -16x² + 261x + 130

Where, x = 8.15625

So, we have

Max height = -16 * 8.15625² + 261 * 8.15625 + 130

Evaluate

Max height = 1194.390625

Approximate

Max height = 1194.39

Hence, the maximum height reached by the rocket is 1194.39 feet

Answer 2

1194.88m

Explanation:

Given the maximum height of the rocket modelled by the expression

y=-16x^2+261x+130

The rocket velocity at its maximum height is zero.

v(x) = dy/dx = 0

dy/dx = -32x + 261

0 = -32x + 261

32x = 261

x = 261/32

x= 8.156secs

Substitute the time into the given expression'

y=-16(8.16)^2+261(8.16)+130

y = -1,064.88 + 2,129.76 + 130

y = 1194.88

Hence the maximum height reached by the rocket is 1194.88m