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Carnegie Mellon University



Problem 12 Medium Difficulty

The record distance in the sport of throwing cowpats is 81.1 $\mathrm{m} .$ This record toss was set by Steve Urner of the United States in 1981 . Assuming the initial launch angle was $45^{\circ}$ and neglecting air resistance, determine (a) the initial speed of the projectile and (b) the total time the projectile was in flight. (c) Qualitatively, how would the answers change if the launch angle were greater than $45^{\circ}$ ? Explain.


a. 28.2$\mathrm { m } / \mathrm { s }$
b. 4.07$\mathrm { s }$
c. both increase


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Mary C.

October 22, 2020

Video Transcript

we can say for part A, we could first say that the total time we know that the vertical velocity of the projectile when the project how returns to the initial launched a level where Delta wise equaling zero meters. We could say that simply velocity y final equals and negative velocity. Why initial So? So you could say that the total time would be equaling um, philosophy? Why final minus velocity? Why initial? And then this would be divided by the acceleration of the wire direction. So this would be equally big brother Negative two the my initial divided by negative G or simply to be why initial divided by G or two times the initial sign of data divided by G. And so we know that the ranges equaling velocity ex initial or velocity ex official most part by tee total. So this would be equaling velocity Initial co sign of theta times to velocity initial signs of fada divided by G. And so this is equaling velocity. Initials squared sine of two Seita divided by G and we can solve for velocity initial. So for party velocity initial is equal in the square root of the range times she divided by signs of to think of this case state has 45 degrees, two times 45 90 degrees side of 90 degrees. We know to be wood, so this is gonna be one. And so our initial velocity is equaling the square root of the range 81.1 meters multiplied by 9.8 meters per second squared and our initial velocity is then found to be 28.2 meters per second. This would be our answer for part A. Now, for part B, we want the total time. Total time is gonna be equally to the initial sign of fate a divided by G. So this would be equal to two times 28 0.2 meters per second, multiplied by side of 45 degrees divided by 9.8 meters per second squared. And the total time is found to be 4.7 seconds. This would be our answer. And for part C, then, um, how would the answers change if the launch angle were greater than 45 degrees? Well, if the it's the angle, the angle, so you could say better yet as the angle increases past 45 degrees. The philosophy initial increases up to fate at equals 90 degrees then, of course, decreases. So that's how they answer would change. That is the end of the solution. Thank you for watching.

Carnegie Mellon University
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