Question

2. A 200-kg boulder has 39,200 joules of gravitational potential energy. What height is it at?

3. A 1-kg model airplane has 12.5 joules of kinetic energy and 98 joules of gravitational potential energy. What is its speed? What is its height?

Answer 1

As per the first question we have to calculate the height at which the boulder is present.

we have been given the mass of the boulder [m] as 200 kg.

The gravitational potential energy is given as 39,000 Joule.

The gravitational potential energy at a height ' h' from the surface earth is given as P.E= mass×height×acceleration due to gravity

The value of g=9.8 m/s^2

Hence height [h]
`=(P.E)/(mg)`

=
`(39000)/(200*9.8) metre`

=19.8979 metre

As per the second question we have to calculate the sped and height of the model airplane.

the mass of model airplane is 1 kg

The kinetic energy [K.E] of the airplane is 12.5 joule

we have K.E
`=(1)/(2) mass*speed^2`

K.E
`=(1)/(2)mv^2`

`v^2=(2K.E )/(m)`

`v^2=(2*12.5)/(1)`

`v=√(25)`

v=5 m/s

Again we have to calculate the height [h]

The potential energy is given as 98 Joule.

we know that P.E= mgh

tex]h=\frac{P.E}{mg}[/tex]

=
`(98)/(1*9.8) metre`

=10 metre

Answer 2

We have that the gravitational energy is given by: U=mgh where m is the mass of the object (in kg), g is the gravitational acceleration and h is the height of the object (in meters). Hence, h=U/(m*g) where g=9.8 m/s^2. Thus, h=20 m if we substitute.
Similarly, substituting in b, we have that the height of the model plane is 10 m. The kinetic energy is given by: K=
`(1)/(2) *m*u^2` where u is the speed of the object. Hence, solving for u we have u=
`√(2K/m)`. Substituting, we have that u=5m/s.