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Carnegie Mellon University

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Problem 37 Medium Difficulty

A father demonstrates projectile motion to his children by placing a pea on his fork's handle and rapidly depressing the curved tines, launching the pea to heights above the dining room table. Suppose the pea is launched at 8.25 $\mathrm{m} / \mathrm{s}$ at an angle of $75.0^{\circ}$ above the table. With what speed does the pea strike the ceiling 2.00 $\mathrm{m}$ above the table?

Answer

$v = 5.37 \mathrm { ms } ^ { - 1 }$

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Fransheska S.

February 24, 2021

Where did the square root of 24.3 come from

Video Transcript

so we know that the initial velocity of the P 8.25 meters per second We also know the angle of launch equaling 75 degrees. Now we can say that the horizontal component of this velocity is gonna be equal in the initial coastline of Fada, this would be eight point to five meters per second coastline of 75 degrees and this is equaling 2.14 meters per second. We can then say that to find the why final. Essentially, we can say that the Y final equals the square root of ve y initial squared plus two times the acceleration times Delta Why? And so this would be equaling. We have the recon say the wife final is simply gonna be equaling the square root of 24.3 meters squared per second squared after plugging in Oliver values. Now here we know that they would be Jean and we can then say that when the P hits the ceiling V, we can save the final. The magnitude would be equaling the square root of the Y final squared plus B X or V X final squared. This would be equal in the square root of 2.14 meters per second quantity squared plus 24.3 meters squared per second squared. And we find that then the magnitude of the final velocity is going to be equaling 5.37 meters per second. This would be our final answer. The speed of the P went hits the ceiling. That is the end of the solution. Thank you for watching.

Carnegie Mellon University
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