A player bounces a 0.43-kg soccer ball off her head, changing the velocity of the ball from 𝐯i=(

Name: Problem 20, Chapter 9: Physics
Uploaded: 2021-03-25T05:52:37-08:00
Duration: 2 min 43 s
Channel: Khoobchandra Agrawal
Description: A player bounces a 0.43-kg soccer ball off her head, changing the velocity of the ball from 𝐯i=(8.8 m / s) x̂+(-2.3 m / s) ŷ to 𝐯f=(5.2 m / s) x̂+(3.7 m / s) ŷ . If the ball is in contact with the player's head for 6.7 ms, what are (a) the direction and (b) the magnitude of the impulse delivered to the ball?

step 1 Hi everyone here it is given mass to be 0 .43 kg initial velocity is 8 .8 i .c. minus 2 .3 j cap

Question

A player bounces a $0.43-\mathrm{kg}$ soccer ball off her head, changing the velocity of the ball from $\overrightarrow{\mathbf{v}}_{i}=(8.8 \mathrm{m} / \mathrm{s}) \hat{\mathrm{x}}+(-2.3 \mathrm{m} / \mathrm{s}) \hat{\mathrm{y}}$ to $\overrightarrow{\mathbf{v}}_{f}=(5.2 \mathrm{m} / \mathrm{s}) \hat{\mathrm{x}}+(3.7 \mathrm{m} / \mathrm{s}) \hat{y} .$ If the ball is in contact with the player's head for $6.7 \mathrm{ms},$ what are (a) the direction and (b) the magnitude of the impulse delivered to the ball?

   A player bounces a $0.43-\mathrm{kg}$ soccer ball off her head, changing the velocity of the ball from $\overrightarrow{\mathbf{v}}_{i}=(8.8 \mathrm{m} / \mathrm{s}) \hat{\mathrm{x}}+(-2.3 \mathrm{m} / \mathrm{s}) \hat{\mathrm{y}}$ to $\overrightarrow{\mathbf{v}}_{f}=(5.2 \mathrm{m} / \mathrm{s}) \hat{\mathrm{x}}+(3.7 \mathrm{m} / \mathrm{s}) \hat{y} .$ If the ball is in contact with the player's head for $6.7 \mathrm{ms},$ what are (a) the direction and (b) the magnitude of the impulse delivered to the ball?

Physics

James S. Walker 4th Edition

Chapter 9, Problem 20

Instant Answer

Solved by Expert Khoobchandra Agrawal

03/25/2021

Step 1

The change in velocity is given by the final velocity minus the initial velocity. In vector form, this is given by: \[\Delta \overrightarrow{\mathbf{v}} = \overrightarrow{\mathbf{v}}_{f} - \overrightarrow{\mathbf{v}}_{i} = (5.2 \hat{\mathrm{x}} + 3.7 Show more…

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A player bounces a $0.43-\mathrm{kg}$ soccer ball off her head, changing the velocity of the ball from $\overrightarrow{\mathbf{v}}_{i}=(8.8 \mathrm{m} / \mathrm{s}) \hat{\mathrm{x}}+(-2.3 \mathrm{m} / \mathrm{s}) \hat{\mathrm{y}}$ to $\overrightarrow{\mathbf{v}}_{f}=(5.2 \mathrm{m} / \mathrm{s}) \hat{\mathrm{x}}+(3.7 \mathrm{m} / \mathrm{s}) \hat{y} .$ If the ball is in contact with the player's head for $6.7 \mathrm{ms},$ what are (a) the direction and (b) the magnitude of the impulse delivered to the ball?

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Key Concepts

Impulse-Momentum Theorem

This theorem states that the impulse delivered to an object is equal to the change in its momentum. It links the applied force over a time interval to the resulting change in the object's velocity, making it a fundamental concept for understanding forces in collisions and other interactions.

Momentum

Momentum is a vector quantity defined as the product of an object's mass and its velocity. In physics, it is a key measure of motion, and changes in momentum are often studied to analyze the effects of forces during collisions or interactions.

Vector Operations in Physics

Since both momentum and velocity are vector quantities, handling them requires the use of vector algebra. This involves operations such as vector subtraction to find the change in momentum, and determining the magnitude and direction of resultant vectors, which are crucial steps in solving problems involving impulse.

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