A ball of mass 33.1 kg is released from rest at a height of 27.6 meters. How fast will the ball be moving just before it hits the ground? (please provide your answer to 1 decimal place)

To find how fast the ball will be moving just before it hits the ground, we can use the principle of conservation of mechanical energy. The potential energy at the height will convert entirely into kinetic energy just before hitting the ground, assuming no energy losses due to air resistance.

The formulas we'll use are:

1. **Potential energy at the top**:  
   \[
   PE = mgh
   \]
   where:
   - \( m \) is the mass of the ball (33.1 kg),
   - \( g \) is the acceleration due to gravity (\(9.8 \, \text{m/s}^2\)),
   - \( h \) is the height (27.6 m).

2. **Kinetic energy just before impact**:  
   \[
   KE = \frac{1}{2}mv^2
   \]
   where \( v \) is the speed of the ball just before it hits the ground.

By energy conservation:
\[
mgh = \frac{1}{2}mv^2
\]

The masses cancel out, leaving:
\[
gh = \frac{1}{2}v^2
\]

Solving for \( v \):
\[
v = \sqrt{2gh}
\]

Substitute the values for \( g \) and \( h \):
\[
v = \sqrt{2 \times 9.8 \times 27.6}
\]
\[
v = \sqrt{540.96}
\]
\[
v \approx 23.3 \, \text{m/s}
\]

So, the ball will be moving at approximately **23.3 m/s** just before it hits the ground.

Would you like further details on the steps or have any questions?

Here are 5 related questions:
1. What happens to the energy if air resistance is considered?
2. How would the speed change if the ball had a different mass?
3. What is the speed of a ball dropped from a height of 50 meters?
4. How long does it take for the ball to hit the ground in this case?
5. What would be the potential energy at the top for this ball?

**Tip:** When using energy conservation, mass cancels out for free-falling objects, meaning the speed at impact depends only on height and gravity, not mass.

A ball of mass 33.1 kg is released from rest at a height of 27.6 meters. How fast will the ball be moving just before it hits the ground?

Learn how to calculate the speed of a 33.1 kg ball released from rest at a height of 27.6 meters just before it hits the ground. Using energy conservation principles, this problem involves kinetic and potential energy formulas. Ideal for students in Grades 9-12.

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