An object is released from rest on a planet that has no atmosphere. The object falls freely for 3.0 meters in the first second. What is the magnitude of the acceleration due to gravity on the planet?

To solve for the magnitude of the acceleration due to gravity on the planet, we can use the following kinematic equation:

\[
d = v_0 t + \frac{1}{2} a t^2
\]

Where:
- \( d \) is the distance fallen (3.0 meters),
- \( v_0 \) is the initial velocity (since the object is released from rest, \( v_0 = 0 \)),
- \( t \) is the time (1 second),
- \( a \) is the acceleration due to gravity (which we are trying to find).

Substituting the known values into the equation:

\[
3.0 = 0 \cdot 1 + \frac{1}{2} a \cdot (1)^2
\]

This simplifies to:

\[
3.0 = \frac{1}{2} a
\]

Multiplying both sides by 2:

\[
6.0 = a
\]

Thus, the magnitude of the acceleration due to gravity on the planet is:

\[
a = 6.0 \, \text{m/s}^2
\]

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:
1. How would the time of fall change if the distance doubled?
2. How would atmospheric drag affect the acceleration of a falling object?
3. What would happen to the object's velocity after 2 seconds of free fall?
4. How can you measure the acceleration due to gravity on Earth using similar principles?
5. What is the difference between mass and weight on this planet?

**Tip:** In free fall problems, the initial velocity is zero if the object is released from rest.

Determine the magnitude of acceleration due to gravity on a planet with no atmosphere by applying kinematic equations. The object falls freely for 3.0 meters in the first second. Suitable for students in Grades 9-10, this problem covers key concepts in kinematics and free fall.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation