Question

what would the gravitational potential energy be of the ball in joules at time 1 second on the graph. dont forget the unit!
time (s) | height (m)
0 | 0
1 | 8
2 | 10
3 | 3

Explanation:

Step1: Recall the formula for gravitational potential energy

The formula for gravitational potential energy is \( PE = mgh \), where \( m \) is the mass of the object, \( g \) is the acceleration due to gravity (\( 9.8 \, \text{m/s}^2 \) on Earth), and \( h \) is the height of the object above a reference point.

Step2: Determine the height at \( t = 1 \, \text{s} \)

From the table, at \( t = 1 \, \text{s} \), the height \( h = 8 \, \text{m} \).

Step3: Assume the mass of the ball (since it's not given, we assume a common mass, e.g., \( m = 1 \, \text{kg} \) for simplicity)

Let \( m = 1 \, \text{kg} \), \( g = 9.8 \, \text{m/s}^2 \), and \( h = 8 \, \text{m} \).

Step4: Calculate the gravitational potential energy

Substitute the values into the formula: \( PE = mgh = 1\times9.8\times8 \).
Calculate \( 9.8\times8 = 78.4 \), so \( PE = 78.4 \, \text{J} \).

Answer:

78.4 J (assuming the mass of the ball is 1 kg, as it's not given. If mass is different, the answer will change. The formula for gravitational potential energy is \( PE = mgh \), where \( g = 9.8 \, \text{m/s}^2 \), \( h = 8 \, \text{m} \) at \( t = 1 \, \text{s} \), and if \( m = 1 \, \text{kg} \), then \( PE = 1\times9.8\times8 = 78.4 \, \text{J} \))