Question

A toy rocket is launched from the top of a building 83 feet tall at an initial velocity of 162 feet per second. a) Give the function that describes the height of the rocket in terms of t. b) Determine the time

Answer 1

Answer:

Step-by-step explanation:

Given

Rocket is Launched From a height of $h=83 ft$

Initial velocity of Rocket $u=162 ft/s$

Considering it is launched vertically upward

therefore height y can be given by

$y=ut+\frac{at^2}{2}$

$y=162t-\frac{32.2t^2}{2}$

Net height as it is launched from a  cliff

$H=h+y$

$H=-16.1t^2+162t+83$

(b)Time to reach maximum height

i.e. at that point velocity is zero

differentiate y w.r.t time and equate to zero

$\frac{\mathrm{d} y}{\mathrm{d} t}=-16.1\times 2t+162$

$2\times 16.1t=162$

$t=\frac{162}{2\times 16.1}=5.03 s$