While a car is stopped at a traffic light in a storm, raindrops strike the roof of the car. The area of the roof is 5.0 m². Each raindrop has a mass of 3.7 × 10^-⁴ kg and speed of 2.5 m/s before impact and is at rest after the impact. If, on average at a given time, 150 raindrops strike each square meter, what is the impulse of the rain striking the car? A)0.69 N . s B)0.046 N . s C)0.14 N . s D)11 N . s E)21 N . s

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Quizplus · Accepted Answer

Impulse is the change in momentum. The momentum of each raindrop is:$$p = mv = (3.7 	imes 10^{-4} 	ext{ kg})(2.5 	ext{ m/s}) = 9.25 	imes 10^{-4} 	ext{ kg m/s}$$The impulse of each raindrop is:$$J = \Delta p = p_f - p_i = 0 - 9.25 	imes 10^{-4} 	ext{ kg m/s} = -9.25 	imes 10^{-4} 	ext{ kg m/s}$$The total impulse is the sum of the impulses of all the raindrops:$$J = (150 	ext{ raindrops/m}^2)(5.0 	ext{ m}^2)(-9.25 	imes 10^{-4} 	ext{ kg m/s}) = -0.69 	ext{ N s}$$The negative sign indicates that the impulse is in the opposite direction of the motion of the raindrops.

While a Car Is Stopped at a Traffic Light in a Storm