Answer: The height of rollercoaster cart above the ground is 1.53 m.
The velocity of rollercoaster cart is 5.29 m/s.
Explanation:
Potential energy is the energy occupied by a substance due to its position. Formula for potential energy is as follows.
P.E = mgh
where,
m = mass of substance
g = gravitational constant = [tex]9.8 m/s^{2}[/tex]
h = height
Substitute the values into above formula as follows.
[tex]P.E = m \times g \times h\\67500 J = 4500 kg \times 9.8 m/s^{2} \times h\\h = \frac{67500 J}{4500 kg \times 9.8 m/s^{2}}\\= 1.53 m[/tex]
Hence, the height of rollercoaster cart above the ground is 1.53 m.
Kinetic energy is the energy occupied by the motion of a substance. Formula for kinetic energy is as follows.
[tex]K.E = \frac{1}{2}m \times v^{2}[/tex]
where,
m = mass of substance
v = velocity of substance
Substitute the values into above formula as follows.
[tex]K.E = \frac{1}{2}m \times v^{2}\\63000 J = \frac{1}{2} \times 4500 kg \times v^{2}\\v^{2} = \frac{63000 J \times 2}{4500 kg}\\v = 5.29 m/s[/tex]
Hence, the velocity of rollercoaster cart is 5.29 m/s.
