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Force of a Baseball Swing. A baseball has mass 0.145 $\mathrm{kg}$ , (a) If the velocity of a pitched ball has a magnitude of 45.0 $\mathrm{m} / \mathrm{s}$ and the batted ball's velocity is 55.0 $\mathrm{m} / \mathrm{s}$ in the opposite direction, find the magnitude of the change in momentum of the ball and of the impulse applied to it by the bat. (b) If the ball remains in contact with the bat for 2.00 $\mathrm{ms}$ , find the magnitude of the average force applied by the bat.

(a) $\vec{J}=\Delta \overrightarrow{\mathrm{p}}=14.5 \mathrm{kg} \cdot \mathrm{m} / \mathrm{s}$

(b) $\sum \overrightarrow{\mathrm{F}}=7250 \mathrm{N}$

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{'transcript': "but we have the most of the best ball. The mass of the best ball is equal to 0.145 kilogram. The biggest ball has speed off 45 point. You don't meter per second, so the speed off bitch to ball is equal to 45 45.0 meters per second. The basketball has a speed of 55.7 meters per second, so the batted ball has a speed equal to 55.0 meters per second in the opposite direction and the time interval different. The ball in contact with the bed is a 2.0 millisecond, so Delta T is equal to 2.0 milli second. Well, we know that it momentum is given by mass times velocity and total. Ford's F is equal to the Tu minus B one divided by a Delta T. Well, let's call this equation number one and this be acquitted. Number two Well, in both momentum to room. Ah, see his feet, uh, in both is equal. Do are changing momentum and change in momentum is final momentum minus initial momentum. Okay, now let's do bark A No, we departed a Let me crawl down. Yes. So here we do park here. Well, first we take the batted balls. Lost is the final velocity and it's directions. The positive direction and we take the pitched balls we lost is the initial velocity. And so it's direction will be the negative direction Eso we have Ah re I is equal to minus 45.0 meters per second and Rieff is equal. Do 55 find zero meter or second are we plug our values for M and initial speed into question number one. So we get the initial momentum off the ball. So initial momentum of the ball is equal to 0.1 for five, uh into minus of 45.0 meter per second on that is equal to minus 6.525 minus 6.5 um 25 You look around me too, per second, right. And similarly, a B two is equal to 0.145 into 55. Find zero. That is equal to 7.975 You look around May 2 per second. It's meter per second, right on the change in momentum. Delta p is equal to be to minus, uh, be one. Well, B two is 7.975 minus into B one. Well, that is minus 6.5 to 5. And therefore change in momentum. Change in momentum is equal to 14.5 our Gilo Kromm meter per second. Okay, All right. And also, we know it in bolts is equal to change in momentum. So impulses able to change in momentum. Therefore, impulse physical too. 14.5. Lucky Luke Graham meter for a second, right? Okay, No, let's do part B. Well, we want to find out on the total force. Well, the total force is equal to 7.975 minus into minus 6.5 to 5. Divided by do 0.0 times 10 to the power minus three. So total force is equal to 7000. About 250 Newton"}