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

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

Step-by-step 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=(1)/(2)mv^2`

`v=\sqrt{(2K)/(m)}`

`v=\sqrt{(2* 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=(u_y)/(2g)`

`s=(u\ sin\theta)/(2g)`

`s=(10.12* sin(45))/(2* 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.