Question

the object has a mass of 7.0 kg. what is the potential energy of the object at point a?
g = 10.00 m/s²
height (m) vs. time (s)
chart: x-axis time (s) from 0 to 4, y-axis height (m) from 0 to 8. line starts at (0,6), peaks, then at point a (1,6), then decreases to (2.5,0), then increases. options: 42 j, 210 j, 420 j

Explanation:

Step1: 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.

Step2: Identify Values

From the graph, at point A, height $h = 6$ m. Mass $m = 7.0$ kg, $g = 10.00$ m/s².

Step3: Substitute Values into Formula

Substitute $m = 7.0$, $g = 10.00$, $h = 6$ into $PE = mgh$:
$PE = 7.0 \times 10.00 \times 6$

Step4: Calculate the Result

$7.0 \times 10.00 = 70$, then $70 \times 6 = 420$? Wait, no—wait, the graph: Wait, point A is at height 6? Wait, no, wait the y-axis is height (m). Wait, the first point is 6, then it goes up to 8, then down to 6 at point A? Wait, no, the graph: at time 1s, point A is at height 6? Wait, no, the y-axis: 6, 8, etc. Wait, no, the coordinates: point A is at (1,6)? Wait, no, the y-axis is height. Wait, the initial height is 6, then it peaks at 8, then at time 1s, point A is at height 6? Wait, no, the red dot is at height 6? Wait, no, the y-axis labels: 2,4,6,8. So point A is at height 6 m? Wait, no, wait the problem: mass 7.0 kg, g=10.00 m/s². Wait, maybe I misread the height. Wait, let's recheck: the graph is Height (m) vs. Time (s). The y-axis: 2,4,6,8. The red dot (point A) is at height 6? Wait, no, maybe it's at height 6? Wait, no, wait the formula: $PE = mgh$. Let's recalculate. If $m = 7$ kg, $g = 10$ m/s², $h = 6$ m: $7 \times 10 \times 6 = 420$? But the options include 420, 210, 42. Wait, maybe I misread the height. Wait, maybe point A is at height 3? No, the graph: at time 1, the height is 6? Wait, no, the first point is (0,6), then it goes up to (some time,8), then down to (1,6)? Wait, no, the x-axis is time (s): 0,1,2,3,4. The y-axis: 2,4,6,8. So at time 1, the height is 6? Wait, no, the red dot is at (1,6). So height h=6 m. Then $PE = 7 \times 10 \times 6 = 420$ J? But wait, maybe the height is 3? No, the y-axis is 6 at that point. Wait, maybe the problem has a typo, or I misread. Wait, no, wait: 7 kg 10 m/s² 6 m = 420 J. But let's check the options: 42 J, 210 J, 420 J. So 420 J is an option. Wait, but maybe I made a mistake. Wait, 7106=420. Yes. So the potential energy is 420 J? Wait, no, wait: 7106=420. So the answer should be 420 J. Wait, but let's check again. Wait, maybe the height is 6? Yes. So the calculation is correct.

Answer:

420 J