**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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Physics

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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Distance and Speed

The speed, distance and time relation forms the basis of study of motion. You will need these concepts in the study of Mechanics. This concept is applicable for students who are studying the following courses –

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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