A 13 kg object is held 6 meters off the ground. How fast will it be going when it hits the ground?



To determine the speed of the object when it hits the ground, we can use the principle of conservation of mechanical energy. The object's potential energy at the height of 6 meters will be completely converted into kinetic energy just before it hits the ground.

The relevant formulas are:

1. **Potential energy (PE)**:  
   \[
   PE = mgh
   \]
   where:
   - \( m \) is the mass of the object (13 kg),
   - \( g \) is the acceleration due to gravity (9.8 m/s²),
   - \( h \) is the height (6 m).

2. **Kinetic energy (KE)**:  
   \[
   KE = \frac{1}{2}mv^2
   \]
   where:
   - \( v \) is the velocity of the object when it hits the ground.

Since energy is conserved, the potential energy at the height will equal the kinetic energy just before impact:
\[
mgh = \frac{1}{2}mv^2
\]

Now we can solve for \( v \):
\[
v = \sqrt{2gh}
\]

Substituting in the known values:
\[
v = \sqrt{2 \times 9.8 \, \text{m/s}^2 \times 6 \, \text{m}}
\]
\[
v = \sqrt{117.6 \, \text{m}^2/\text{s}^2}
\]
\[
v \approx 10.84 \, \text{m/s}
\]

Thus, the object will be moving at approximately **10.84 m/s** when it hits the ground.

Would you like a more detailed breakdown or have any other questions?

### Related Questions:
1. How would the speed change if the object were dropped from a higher height?
2. What would happen if air resistance were considered in this problem?
3. How can we calculate the time it takes for the object to reach the ground?
4. How does the mass of the object affect its speed upon hitting the ground?
5. What is the kinetic energy of the object just before it hits the ground?

### Tip:
In problems involving free fall, the mass of the object doesn't affect its final velocity—only the height and gravitational acceleration matter, as long as air resistance is negligible.

A 13 kg object is held 6 meters off the ground. How fast will it be going when it hits the ground?

Calculate the velocity of a 13 kg object dropped from a height of 6 meters using the conservation of mechanical energy. Learn the key concepts of potential and kinetic energy with a step-by-step solution. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation