Question

A rocket is shot straight into the air at an initial velocity of 70 feet/second.

The height of the rocket after t seconds is represented by the formula
h = 70t - 5tº. What is the maximum height the rocket reaches?
235 feet
265 feet
215 feet
245 feet

Answer 1

Answer: 245 feet

Explanation:

Given: The height of the rocket after t seconds is represented by the formula:

`h=70t-5t^2`

`(dh)/(dt)=70-10t` [Differentiate both sides w.r.t. t]

Put

`(dh)/(dt)=0\\\\\Rightarrow\ 70-10t=0\\\\\Rightarrow\ t=(70)/(10)=7`

Also,
`(d^2h)/(dt^2)=-10<0` i.e. height is maximum at t=7.

Maximum height =
`h=70(7)-5(7)^2 = 490 - 245= 245\text{ feet}`

Hence, the maximum height the rocket reaches = 245 feet.