Question

ella has a mass of 56 kg, and tyrone has a mass of 68 kg. ella is standing at the top of a skateboard ramp that is 1.5 meters tall. which conclusion is best supported by the given information? if tyrone stands at the top of the same ramp, his potential energy will be less than ellas. if tyrone stands at the top of a 1 m high ramp, his potential energy will be greater than ellas. if tyrone stands at the top of the same ramp, his potential energy will be the same as ellas. if tyrone stands at the top of a 2 m high ramp, his potential energy will be greater than ellas.

Explanation:

Step1: Recall potential - energy formula

The formula for gravitational potential energy is $U = mgh$, where $m$ is mass, $g$ is the acceleration due to gravity ($g\approx9.8\ m/s^{2}$), and $h$ is height.

Step2: Analyze Ella's potential energy

Ella's mass $m_{E}=56\ kg$ and height $h_{E} = 1.5\ m$, so her potential energy $U_{E}=m_{E}gh_{E}=56\times g\times1.5 = 84g$.

Step3: Analyze Tyrone's potential energy in different cases

Tyrone's mass $m_{T}=68\ kg$.

• If Tyrone stands at the top of the same 1.5 - m ramp, his potential energy $U_{T}=m_{T}gh_{T}=68\times g\times1.5=102g>U_{E}$.
• If Tyrone stands at the top of a 1 - m high ramp, $U_{T}=m_{T}gh_{T}=68\times g\times1 = 68g
• If Tyrone stands at the top of a 2 - m high ramp, $U_{T}=m_{T}gh_{T}=68\times g\times2 = 136g>U_{E}$.

Answer:

If Tyrone stands at the top of a 2 m high ramp, his potential energy will be greater than Ella's.