Question

A toy rocket, launched from the ground, rises vertically with an acceleration of 18 m/s^2 for 18 s until its motor stops. Disregarding any air resistance, what max- imum height above the ground will the rocket achieve? The acceleration of gravity is 9.8 m/s^2. Answer in units of km.

Answer 1

Answer:

8271.92 m

Explanation:

t = Time taken

u = Initial velocity

v = Final velocity

s = Displacement

a = Acceleration

Equation of motion

$s=ut+\frac{1}{2}at^2\\\Rightarrow s=0\times t+\frac{1}{2}\times 18\times 18^2\\\Rightarrow s=2916\ m$

The height reached at 18 seconds is 2916 m

$v=u+at\\\Rightarrow v=0+18\times 18\\\Rightarrow v=324\ m/s$

The velocity at 2916 m is 324 m/s

$v^2-u^2=2as\\\Rightarrow s=\frac{v^2-u^2}{2a}\\\Rightarrow s=\frac{0^2-324^2}{2\times -9.8}\\\Rightarrow s=5355.92\ m$

Maximum height reached by the toy rocket is 2916+5355.92 = 8271.92 m