Question

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

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]$=\frac{P.E}{mg}$

                              =$\frac{39000}{200*9.8} metre$

                              =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$=\frac{1}{2} mass*speed^2$

                K.E$=\frac{1}{2}mv^2$

                 $v^2=\frac{2K.E }{m}$

                  $v^2=\frac{2*12.5}{1}$

                    $v=\sqrt{25}$

                      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]  

                       =$\frac{98}{1*9.8} metre$

                       =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=$\frac{1}{2} *m*u^2$ where u is the speed of the object. Hence, solving for u we have u=$\sqrt{2K/m}$. Substituting, we have that u=5m/s.