Question

5.

Answer 1

1) The gravitational potential energy of the child is 68 J

2) The child is 0.25 m above the ground

Explanation:

1)

The mechanical energy of a body is equal to the sum between its gravitational potential energy (PE) and its kinetic energy (KE):

$E=PE+KE$ (1)

In this problem, we know that

E = 315 J is the total mechanical energy of the child

Its kinetic energy is given by

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

where

m = 28 kg is his mass

v = 4.2 m/s is his speed

Substituting,

$K=\frac{1}{2}(28)(4.2)^2=247.0 J$

Substituting into (1), we can now find the potential energy of the child:

$PE=E-KE=315-247=68 J$

2)

The gravitational potential energy of an object is given by

$PE=mgh$

where

m is the mass

g is the gravitational acceleration

h is the height above the ground

For the child in this problem,

m = 28 kg

$g=9.8 m/s^2$

and we know the value of its potential energy, PE = 68 J, therefore we can find his height above the ground:

$h=\frac{PE}{mg}=\frac{68}{(28)(9.8)}=0.25 m$

Learn more about potential energy:

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