https://file.aiquickdraw.com/mathbot/file/1729615276583qbm9fxez.jpg

To solve this problem, we can use the following kinematic equation that relates initial velocity (\(v_0\)), final velocity (\(v_f\)), acceleration (\(a\)), and displacement (\(d\)):

\[
v_f^2 = v_0^2 + 2ad
\]

Where:
- \(v_0 = 50.0 \, \text{m/s}\) (the initial velocity),
- \(a = 9.8 \, \text{m/s}^2\) (the acceleration due to gravity),
- \(d = 155 \, \text{m}\) (the height of the building).

We need to find \(v_f\), the final velocity. Rearranging the equation to solve for \(v_f\):

\[
v_f = \sqrt{v_0^2 + 2ad}
\]

Now, let's substitute the values:

\[
v_f = \sqrt{(50.0)^2 + 2(9.8)(155)}
\]

\[
v_f = \sqrt{2500 + 2(9.8)(155)}
\]

\[
v_f = \sqrt{2500 + 3038}
\]

\[
v_f = \sqrt{5538}
\]

\[
v_f \approx 74.41 \, \text{m/s}
\]

So, the final velocity of the rock as it hits the ground is approximately **74.41 m/s**.

Would you like a more detailed explanation of the steps or have any other questions?

Here are 5 related questions:
1. How would the final velocity change if the rock were thrown upwards instead of downwards?
2. What if the rock were dropped from rest, how would that affect the final velocity?
3. How long does it take for the rock to reach the ground?
4. How would air resistance affect the final velocity in real-life situations?
5. What is the maximum height reached if the rock is thrown upwards at the same speed?

**Tip:** In kinematic problems, always check whether acceleration is constant (like gravity) to use the right formulas.

A rock is thrown downward from the top of a 155 m tall building at 50.0 m/s. What is the final velocity of the rock as it hits the ground?

Solve for the final velocity of a rock thrown downward at 50.0 m/s from a 155 m tall building using kinematic equations. Learn key concepts in physics related to motion and acceleration due to gravity. Suitable for Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation