Question

Please help!! giving a lot of points

A rollercoaster cart that has a mass of 4500 kg has 67.5 kJ (kilojoules), or 67,500 J (joules), of gravitational potential
energy. What is its height above the ground?


PT.2

The same 4500 kg rollercoaster cart is moving with 63.0 kJ (kilojoules), or 63,000 J (joules), of kinetic energy at the


bottom of its biggest hill. What is its velocity?

Answer 1

Question 1.

• mass = 4500 kg
• potential energy (p.e) = 67500 J

now, we know :

=》

`p.e = mgh`

=》

`67500 = 4500 * 10 * h`

=》

`67500 = 45000 * h`

=》

`h = (67500)/(45000)`

=》

`h = 1.5 \: m`

note : if we take acceleration due to gravity as 9.8, then height = 1.53 m

Question 2.

• mass = 4500 kg
• kinetic energy = 63000 j

we know,

=》

`k.e = (1)/(2) mv {}^(2)`

=》

`63000 = (1)/(2) * 4500 * {v}^(2)`

=》

`{v}^(2) = (63000 * 2)/(4500)`

=》

`{v}^(2) = 28`

=》

`v = √(28)`

=》

`v = 2 √(7) \: \: ms {}^( - 1)`

or

=》

`5.29 \: \: ms {}^( - 1)`