Question

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

Answer 1

Answer: 245 feet

Step-by-step explanation:

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

$h=70t-5t^2$

$\dfrac{dh}{dt}=70-10t$  [Differentiate both sides w.r.t. t]

Put

$\dfrac{dh}{dt}=0\\\\\Rightarrow\ 70-10t=0\\\\\Rightarrow\ t=\dfrac{70}{10}=7$

Also, $\dfrac{d^2h}{dt^2}=-10$ 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.