Question

the table shows information about four objects resting at the top of a hill. four objects at rest on a hill object mass (kg) potential energy (j) w 50 980 x 35 1,029 y 62 1,519 z 24 1,176 which object is on the tallest hill?

Explanation:

Step1: Recall potential - energy formula

The gravitational potential - energy formula is $PE = mgh$, where $PE$ is potential energy, $m$ is mass, $g$ is the acceleration due to gravity ($g = 9.8\ m/s^{2}$), and $h$ is height. We can solve for $h=\frac{PE}{mg}$.

Step2: Calculate height for object W

For object W, $m = 50\ kg$ and $PE = 980\ J$. Then $h_W=\frac{PE_W}{m_Wg}=\frac{980}{50\times9.8}=\frac{980}{490}=2\ m$.

Step3: Calculate height for object X

For object X, $m = 35\ kg$ and $PE = 1029\ J$. Then $h_X=\frac{PE_X}{m_Xg}=\frac{1029}{35\times9.8}=\frac{1029}{343}=3\ m$.

Step4: Calculate height for object Y

For object Y, $m = 62\ kg$ and $PE = 1519\ J$. Then $h_Y=\frac{PE_Y}{m_Yg}=\frac{1519}{62\times9.8}=\frac{1519}{607.6}\approx2.5\ m$.

Step5: Calculate height for object Z

For object Z, $m = 24\ kg$ and $PE = 1176\ J$. Then $h_Z=\frac{PE_Z}{m_Zg}=\frac{1176}{24\times9.8}=\frac{1176}{235.2}=5\ m$.

Answer:

Z