3. Jennie dropped 2.5 kg of block from a certain height and fell for 5 seconds. Find the potential energy of the block. Round off your answer in 4 significant figures.

To find the potential energy of the block, we can use the formula:

\[
PE = mgh
\]

where:
- \(PE\) is the potential energy (in joules),
- \(m\) is the mass of the object (in kg),
- \(g\) is the acceleration due to gravity (approximately \(9.81 \, \text{m/s}^2\)),
- \(h\) is the height from which the block is dropped (in meters).

### Step 1: Calculate the height
Since the time of the fall is given (5 seconds), we can find the height using the equation for distance in free fall:

\[
h = \frac{1}{2} g t^2
\]

Substitute the known values (\(g = 9.81 \, \text{m/s}^2\) and \(t = 5 \, \text{seconds}\)):

\[
h = \frac{1}{2} (9.81) (5^2) = 0.5 \times 9.81 \times 25 = 122.625 \, \text{meters}
\]

### Step 2: Calculate the potential energy
Now, substitute the mass (\(m = 2.5 \, \text{kg}\)), the height (\(h = 122.625 \, \text{m}\)), and \(g = 9.81 \, \text{m/s}^2\)) into the formula for potential energy:

\[
PE = 2.5 \times 9.81 \times 122.625 = 3009.24 \, \text{J}
\]

### Step 3: Round to 4 significant figures
Rounding the result to 4 significant figures:

\[
PE \approx 3010 \, \text{Joules}
\]

Thus, the potential energy of the block is approximately **3010 J**.

Would you like a detailed breakdown of any step or further clarifications?

### Related Questions:
1. How would the potential energy change if the mass of the block was doubled?
2. What would the potential energy be if the block was dropped from a height of 100 meters instead of 122.625 meters?
3. How does the time of fall affect the potential energy of the block?
4. What is the kinetic energy of the block just before hitting the ground?
5. How would the calculation change if the fall happened on a planet with a different gravitational acceleration?

### Tip:
Remember, potential energy only depends on the height and not on the time it takes for the object to fall.

Jennie dropped 2.5 kg of block from a certain height and fell for 5 seconds. Find the potential energy of the block. Round off your answer in 4 significant figures.

Learn how to calculate the potential energy of a 2.5 kg block dropped from a height, falling for 5 seconds. This step-by-step solution involves key physics concepts like potential energy, free fall, and the use of PE = mgh formula. Suitable for students in Grades 9-12.

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