**Physics Problem: Projectile Launcher Speed Calculation****Problem Statement:**For a projectile launcher, the spring is compressed by 5 cm, storing elastic energy in its spring with stiffness \( k = 50 \, \text{N/cm} \). With what speed does the launcher launch a 100 gram ball?**Answer Options:**- 5 m/s- 50 m/s- 0.5 m/s- None of these are correct**Explanation:**To solve this problem, you would need to consider the conservation of energy. The potential energy stored in the compressed spring is converted into the kinetic energy of the ball:\[ \text{Potential Energy} = \frac{1}{2} k x^2 \]\[ \text{Kinetic Energy} = \frac{1}{2} mv^2 \]Where:- \( k \) is the spring constant in N/cm,- \( x \) is the compression distance in meters,- \( m \) is the mass of the ball in kilograms,- \( v \) is the velocity of the ball.Calculate the speed of the ball using these equations to find the correct answer.

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Answered: 5 m/s 50 m/s 0.5 m/s None of these are…

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5 m/s 50 m/s 0.5 m/s None of these are correct

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

**Physics Problem: Projectile Launcher Speed Calculation**

**Problem Statement:**

For a projectile launcher, the spring is compressed by 5 cm, storing elastic energy in its spring with stiffness \( k = 50 \, \text{N/cm} \). With what speed does the launcher launch a 100 gram ball?

**Answer Options:**

- 5 m/s
- 50 m/s
- 0.5 m/s
- None of these are correct

**Explanation:**

To solve this problem, you would need to consider the conservation of energy. The potential energy stored in the compressed spring is converted into the kinetic energy of the ball:

\[ \text{Potential Energy} = \frac{1}{2} k x^2 \]

\[ \text{Kinetic Energy} = \frac{1}{2} mv^2 \]

Where:
- \( k \) is the spring constant in N/cm,
- \( x \) is the compression distance in meters,
- \( m \) is the mass of the ball in kilograms,
- \( v \) is the velocity of the ball.

Calculate the speed of the ball using these equations to find the correct answer.

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