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
Accepted Solution
A:
Answer:Step-by-step explanation:GivenRocket is Launched From a height of [tex]h=83 ft[/tex]Initial velocity of Rocket [tex]u=162 ft/s[/tex]Considering it is launched vertically upwardtherefore height y can be given by [tex]y=ut+\frac{at^2}{2}[/tex][tex]y=162t-\frac{32.2t^2}{2}[/tex]Net height as it is launched from a cliff[tex]H=h+y[/tex][tex]H=-16.1t^2+162t+83[/tex](b)Time to reach maximum heighti.e. at that point velocity is zerodifferentiate y w.r.t time and equate to zero[tex]\frac{\mathrm{d} y}{\mathrm{d} t}=-16.1\times 2t+162[/tex][tex]2\times 16.1t=162[/tex][tex]t=\frac{162}{2\times 16.1}=5.03 s[/tex]