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Carnegie Mellon University

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Problem 9 Medium Difficulty

The best leaper in the animal kingdom is the puma, which can jump to a height of 3.7 $\mathrm{m}$ when leaving the ground at an angle of $45^{\circ} .$ With what speed must the animal leave the ground to reach that height?

Answer

$t _ { 0 } = 12.04 \mathrm { ms } ^ { - 1 }$

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Video Transcript

here at the maximum height, we can say the why equals zero or we can save the Y Final equal zero meters per second at max height. And then we can say the time to reach this height. We can save me. Why Final equals V. Why initial plus the acceleration of our direction Times t Or we can say t would simply be equaling V. Why final minus the Why initial divided by case of why we know that the final velocity would then be zero and this would be equal to Negative V. Why initial really negative view our initial divided by negative g and this is equaling the why initial over G. And so the vertical displacement occurred during this time we can say don't know why Max would be equaling V. Why average multiplied by tea or the why final plus v. Why initial over two multiplied by TV. Why final? We know to be zero. So this would be simply equaling the why initial over two multiplied by the why initial over G and this is equaling V. Why initial squared divided by two G. This would be for the rather. This would simply be ah, equation for the vertical displacement during that time during that upward upward path. Essentially now, if the maximum height Delta y Max is equaling 3.7 meters, then we can see that then V Why initial would be equaling the square root of two g delta? Why, Max? So this would be equal in the square root of two multiplied by 9.80 meters per second squared. This would be multiplied by 3.7 meters and this would be equaling 28 and 1/2 8.5 meters per second. Now if the angle of projection is 45 degrees, so essentially the angle of launch, that means that the launch speed, the initial would be equaling the why initial divided by sign of failure. And so this would be equaling 8.5 meters for a second divided by sign of 45 degrees, and we find that then the initial is equaling 12 meters per second. This would be our final answer. That is the end of the solution. Thank you for watching

Carnegie Mellon University
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