Question

A toy rocket, mass 0.8 kg, blasts up at a 45 degrees from ground level with a kinetic energy of 41 J. To what maximum vertical height does it rise?

Answer 1

Answer:

The maximum height reached by the toy rocket is 0.73 meters.

Explanation:

It is given that,

Mass of the toy rocket, m = 0.8 kg

It is projected at an angle of 45 degrees from ground level. The kinetic energy of the rocket is used to find the velocity with which it was projected as :

$K=\dfrac{1}{2}mv^2$

$v=\sqrt{\dfrac{2K}{m}}$

$v=\sqrt{\dfrac{2\times 41}{0.8}}$        

u = 10.12 m/s

When it reaches to a maximum height, its final velocity will be equal to 0, v = 0

Using third equation of motion to find it as :

$v^2-u^2=2as$

a = -g

$-u^2=-2gs$

s is the maximum height reached by the toy rocket

In vertical direction, $u_y=u\ sin\theta$

$s=\dfrac{u_y}{2g}$

$s=\dfrac{u\ sin\theta}{2g}$

$s=\dfrac{10.12\times sin(45)}{2\times 9.8}$

s = 0.36 meters

So, the maximum height reached by the toy rocket is 0.73 meters. Hence, this is the required solution.