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Define impulse. State its S.I. unit. State and prove impulse-momentum theorem. A batsman deflects a ball by an angle of 45 without changing its initial speed which is equal to 54Kmhr1. What is the impulse imparted to the ball (Mass of the ball is 0.15kg)?

Answer
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Hint: Impulse can be described as the change in momentum of an object to which force is implemented. An object in the behaviour of any force accelerates or changes the velocity. The same force appearing on the same body for a long time will produce a more significant change in its linear momentum than the equivalent for a short duration.

Complete step by step answer:
 Impulse defined as a force applied on an object for a short duration of time. Its S.I. unit is Ns. It is defined as the 1 N force applied on a body for one second of time.
Impulse-momentum theorem states that Impulse applying on a body changes the same amount of linear momentum and change will occur in the same direction.
Proof: -
Let J is the impulse that produced between time t1 and t2.
F is the force acting in the time interval of t1 and t2.
We can write as –
J=t1t2Fdt
By Newton’s second law, Force and momentum can related as-
F=dpdt
J=t1t2dpdtdt
J=p1p2dp
J=p2p1
Hence proved, impulse is equal to the change in linear momentum.
Given: - initial speed, u =54Kmhr1=54×518=15ms1
Initial speed is equal to final speed.
Mass of the ball = 0.15Kg
Ball is deviated at 45 but the angle with the x-axis will be 22.5.
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Initial momentum of ball = mucosθ along PR
Final momentum of ball = mucosθ along RP
 Impulse=Change in momentum
J=2mucosθ
 J=2×0.15×15×cosθ
J=4.16Kgms1
Impulse imparted to the ball = 4.16Kgms1

Note: A small force acted for a long span will produce the same change in momentum as an Impulse force for a small duration. Forces which are acted over a short time interval are called impulsive forces. Impulse is a vector quantity. It arises basically during the collision.
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