Question

the object has a mass of 9.0 kg. what is the potential energy of the object at point a?
g = 10.00 m/s²
height (m) vs. time (s)
options: 180 j, 360 j, 36 j

Explanation:

Step1: Identify height at point A

From the graph, at point A (time = 3 s), the height \( h = 4 \, \text{m} \).

Step2: Recall potential energy formula

The formula for gravitational potential energy is \( PE = mgh \), where \( m \) is mass, \( g \) is acceleration due to gravity, and \( h \) is height.

Step3: Substitute values into formula

Given \( m = 9.0 \, \text{kg} \), \( g = 10.00 \, \text{m/s}^2 \), \( h = 4 \, \text{m} \).
\( PE = 9.0 \times 10.00 \times 4 \)
\( PE = 9.0 \times 40 \)
\( PE = 360 \, \text{J} \)? Wait, no—wait, 9104: 910=90, 904=360? Wait, no, wait the height at A: looking at the graph, the y-axis is height (m). At time 3s, the height is 4m? Wait, no, the first peak is at 8m, then at time 3s, the height is 4m? Wait, no, let's check again. Wait, the graph: x-axis time (s), y-axis height (m). At time 3s, the point A is at height 4m? Wait, no, maybe I misread. Wait, the options: 180, 360, 36. Wait, 9104=360? But maybe the height is 4m? Wait, no, wait the first peak is 8m at t=1s, then at t=3s, the height is 4m? Wait, let's recalculate. Wait, \( m = 9 \, \text{kg} \), \( g = 10 \, \text{m/s}^2 \), \( h = 4 \, \text{m} \). So \( PE = 9 \times 10 \times 4 = 360 \)? But the third option is 36. Wait, maybe I misread the height. Wait, maybe the height at A is 4m? Wait, no, maybe the height is 4m? Wait, no, let's check the graph again. The y-axis: 0,2,4,6,8. At time 3s, the height is 4m (since the point A is at (3,4)). So \( h = 4 \, \text{m} \). Then \( PE = 9 \times 10 \times 4 = 360 \)? But the options include 360. Wait, but maybe I made a mistake. Wait, no, 9104: 910=90, 904=360. So the potential energy is 360 J? Wait, but let's check again. Wait, maybe the height is 4m? Wait, the graph: at time 3s, the height is 4m. So yes. So the calculation is \( PE = mgh = 9 \times 10 \times 4 = 360 \, \text{J} \). Wait, but the third option is 36. Wait, maybe I misread the height. Wait, maybe the height is 4m? Wait, no, maybe the height is 4m, but 9104=360. So the correct answer should be 360 J? Wait, but let's check the options. The middle option is 360 J. So that's the answer.

Wait, no, wait—wait, 9 kg, g=10, h=4: 910=90, 904=360. Yes. So the potential energy is 360 J.

Answer:

360 J (corresponding to the middle option: 360 J)