A batsman deflects a ball by an angle of 45^∘ without changing its initial speed which is equal

step 1 In this problem, a bat is going to hit a ball which is coming towards the bat at a speed of 54 k

A batsman deflects a ball by an angle of 45^∘ without...

A batsman deflects a ball by an angle of $45^{\circ}$ without changing its initial speed which is equal to $54 \mathrm{~km} / \mathrm{h}$. What is the impulse imparted to the ball? (Mass of the ball is $0.15$ kg.)

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Key Concepts

Impulse

Impulse is the vector quantity that represents the change in momentum of an object, often resulting from an applied force over a period of time. It is defined mathematically as the integral of force with respect to time or, in situations with a sudden change, as the difference between final and initial momentum.

Momentum

Momentum is the product of an object's mass and its velocity. As a vector quantity, momentum not only has magnitude but also a direction, and changes in either can represent the effect of forces acting on the object.

Vector Analysis

In problems involving changes in direction, it is crucial to treat quantities like velocity and momentum as vectors. This involves decomposing them into components, applying trigonometric relationships, and then determining the resultant vector, which is essential for calculating changes in momentum.

Unit Conversion

Consistent units are essential in physics calculations. Converting all measurements to a standard unit system, such as meters per second for velocity, ensures that the calculations involving mass, velocity, and subsequently momentum and impulse are accurate and consistent.

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