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?
o if tyrone stands at the top of the same ramp, his potential energy will be less than ellas.
o if tyrone stands at the top of a 1 m high ramp, his potential energy will be greater than ellas.
o if tyrone stands at the top of the same ramp, his potential energy will be the same as ellas.
o if tyrone stands at the top of a 2 m high ramp, his potential energy will be greater than ellas.

Explanation:

Step1: Recall the potential energy formula

The formula for gravitational potential energy is \(U = mgh\), where \(m\) is mass, \(g\) is the acceleration due to gravity (\(g = 9.8\space m/s^{2}\)), and \(h\) is height.

Step2: Analyze each option

• Option 1:

If they are at the same ramp (\(h\) is the same), \(m_{Ella}=56\space kg\), \(m_{Tyrone} = 68\space kg\). Using \(U=mgh\), since \(m_{Tyrone}>m_{Ella}\) and \(h\) and \(g\) are the same, \(U_{Tyrone}>U_{Ella}\). So this option is wrong.

• Option 2:

For Ella, \(U_{Ella}=m_{Ella}gh_{Ella}=56\times9.8\times1.5 = 56\times14.7=823.2\space J\). For Tyrone, \(U_{Tyrone}=m_{Tyrone}gh_{Tyrone}=68\times9.8\times1=666.4\space J\). Since \(823.2>666.4\), this option is wrong.

• Option 3:

Using \(U = mgh\), with \(h\) same, \(m\) different (\(m_{Tyrone}>m_{Ella}\)), \(U\) values are different. So this option is wrong.

• Option 4:

For Ella, \(U_{Ella}=m_{Ella}gh_{Ella}=56\times9.8\times1.5=823.2\space J\). For Tyrone, \(U_{Tyrone}=m_{Tyrone}gh_{Tyrone}=68\times9.8\times2=68\times19.6 = 1332.8\space J\). Since \(1332.8>823.2\), this option is correct.

Answer:

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