**Title: Elastic Collision Analysis Between a Soccer Ball and a Golf Ball** **Introduction:** Consider a scenario where a 0.80-kg soccer ball traveling at 20 m/s makes a head-on elastic collision with a 0.050 kg golf ball initially at rest. For the purpose of this analysis, we will ignore friction, gravity, and any other external forces. **a) Relative Velocity After Collision:** To find out by how much the golf ball is moving faster than the soccer ball after the collision, we use the relative velocity formula: \[ U_{12} = v_1 - v_2 = 20 \text{ m/s} - 0 \text{ m/s} = 20 \text{ m/s} \] **b) Speed of the Soccer Ball After Collision:** The velocity of the soccer ball immediately after the collision is calculated using the formula: \[ v_3 = \frac{mv}{m+M} \] Substituting the values: \[ v_3 = \frac{0.80 \text{ kg} \times 20 \text{ m/s}}{0.80 \text{ kg} + 0.050 \text{ kg}} = \frac{16 \text{ kg m/s}}{0.85 \text{ kg}} = 18.8235 \text{ m/s} \] **c) Speed of the Golf Ball After Collision:** The velocity of the golf ball immediately after the collision is calculated as: \[ v_3 = \frac{mv}{m+M} \] Substituting the values: \[ v_3 = \frac{0.050 \text{ kg} \times 20 \text{ m/s}}{0.050 \text{ kg} + 0.80 \text{ kg}} = \frac{1 \text{ kg m/s}}{0.85 \text{ kg}} = 1.17647 \text{ m/s} \] **Conclusion:** Through these calculations, we determine the outcome of an elastic collision between a soccer ball and a golf ball. The velocities indicate how both balls respond post-collision in an ideal scenario where external forces are negligible.
**Title: Elastic Collision Analysis Between a Soccer Ball and a Golf Ball** **Introduction:** Consider a scenario where a 0.80-kg soccer ball traveling at 20 m/s makes a head-on elastic collision with a 0.050 kg golf ball initially at rest. For the purpose of this analysis, we will ignore friction, gravity, and any other external forces. **a) Relative Velocity After Collision:** To find out by how much the golf ball is moving faster than the soccer ball after the collision, we use the relative velocity formula: \[ U_{12} = v_1 - v_2 = 20 \text{ m/s} - 0 \text{ m/s} = 20 \text{ m/s} \] **b) Speed of the Soccer Ball After Collision:** The velocity of the soccer ball immediately after the collision is calculated using the formula: \[ v_3 = \frac{mv}{m+M} \] Substituting the values: \[ v_3 = \frac{0.80 \text{ kg} \times 20 \text{ m/s}}{0.80 \text{ kg} + 0.050 \text{ kg}} = \frac{16 \text{ kg m/s}}{0.85 \text{ kg}} = 18.8235 \text{ m/s} \] **c) Speed of the Golf Ball After Collision:** The velocity of the golf ball immediately after the collision is calculated as: \[ v_3 = \frac{mv}{m+M} \] Substituting the values: \[ v_3 = \frac{0.050 \text{ kg} \times 20 \text{ m/s}}{0.050 \text{ kg} + 0.80 \text{ kg}} = \frac{1 \text{ kg m/s}}{0.85 \text{ kg}} = 1.17647 \text{ m/s} \] **Conclusion:** Through these calculations, we determine the outcome of an elastic collision between a soccer ball and a golf ball. The velocities indicate how both balls respond post-collision in an ideal scenario where external forces are negligible.
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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Solve the first problem: includes a, b, and c.
![**Title: Elastic Collision Analysis Between a Soccer Ball and a Golf Ball**
**Introduction:**
Consider a scenario where a 0.80-kg soccer ball traveling at 20 m/s makes a head-on elastic collision with a 0.050 kg golf ball initially at rest. For the purpose of this analysis, we will ignore friction, gravity, and any other external forces.
**a) Relative Velocity After Collision:**
To find out by how much the golf ball is moving faster than the soccer ball after the collision, we use the relative velocity formula:
\[
U_{12} = v_1 - v_2 = 20 \text{ m/s} - 0 \text{ m/s} = 20 \text{ m/s}
\]
**b) Speed of the Soccer Ball After Collision:**
The velocity of the soccer ball immediately after the collision is calculated using the formula:
\[
v_3 = \frac{mv}{m+M}
\]
Substituting the values:
\[
v_3 = \frac{0.80 \text{ kg} \times 20 \text{ m/s}}{0.80 \text{ kg} + 0.050 \text{ kg}} = \frac{16 \text{ kg m/s}}{0.85 \text{ kg}} = 18.8235 \text{ m/s}
\]
**c) Speed of the Golf Ball After Collision:**
The velocity of the golf ball immediately after the collision is calculated as:
\[
v_3 = \frac{mv}{m+M}
\]
Substituting the values:
\[
v_3 = \frac{0.050 \text{ kg} \times 20 \text{ m/s}}{0.050 \text{ kg} + 0.80 \text{ kg}} = \frac{1 \text{ kg m/s}}{0.85 \text{ kg}} = 1.17647 \text{ m/s}
\]
**Conclusion:**
Through these calculations, we determine the outcome of an elastic collision between a soccer ball and a golf ball. The velocities indicate how both balls respond post-collision in an ideal scenario where external forces are negligible.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd9ac933e-a222-4210-8a67-76a29c4a48c0%2F236be5a2-2631-4be3-99a8-a02158fb8795%2Fuj0k2bs_processed.png&w=3840&q=75)
Transcribed Image Text:**Title: Elastic Collision Analysis Between a Soccer Ball and a Golf Ball**
**Introduction:**
Consider a scenario where a 0.80-kg soccer ball traveling at 20 m/s makes a head-on elastic collision with a 0.050 kg golf ball initially at rest. For the purpose of this analysis, we will ignore friction, gravity, and any other external forces.
**a) Relative Velocity After Collision:**
To find out by how much the golf ball is moving faster than the soccer ball after the collision, we use the relative velocity formula:
\[
U_{12} = v_1 - v_2 = 20 \text{ m/s} - 0 \text{ m/s} = 20 \text{ m/s}
\]
**b) Speed of the Soccer Ball After Collision:**
The velocity of the soccer ball immediately after the collision is calculated using the formula:
\[
v_3 = \frac{mv}{m+M}
\]
Substituting the values:
\[
v_3 = \frac{0.80 \text{ kg} \times 20 \text{ m/s}}{0.80 \text{ kg} + 0.050 \text{ kg}} = \frac{16 \text{ kg m/s}}{0.85 \text{ kg}} = 18.8235 \text{ m/s}
\]
**c) Speed of the Golf Ball After Collision:**
The velocity of the golf ball immediately after the collision is calculated as:
\[
v_3 = \frac{mv}{m+M}
\]
Substituting the values:
\[
v_3 = \frac{0.050 \text{ kg} \times 20 \text{ m/s}}{0.050 \text{ kg} + 0.80 \text{ kg}} = \frac{1 \text{ kg m/s}}{0.85 \text{ kg}} = 1.17647 \text{ m/s}
\]
**Conclusion:**
Through these calculations, we determine the outcome of an elastic collision between a soccer ball and a golf ball. The velocities indicate how both balls respond post-collision in an ideal scenario where external forces are negligible.
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