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Carnegie Mellon University

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Problem 44 Hard Difficulty

A $2.00-\mathrm{m}$ -tall basketball player is standing on the floor 10.0 $\mathrm{m}$ from the basket, as in Figure $\mathrm{P} 3.44$ . If he shoots the ball at a $40.0^{\circ}$ angle with the horizontal, at what initial speed must he throw the basketball so that it goes through the hoop without striking the backboard? The height of the basket is 3.05 $\mathrm{m} .$

Answer

10.7$\mathrm { m } / \mathrm { s }$

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Video Transcript

so essentially here. We want to figure out as we need equations as we possibly can and at the animal have a system of equations that we can solve for So we can say first that Delta Y is equaling V. Why initial t plus 1/2 GT squared and in this case we're gonna say that upwards is positive and so it upwards is positive. The ball needs to be traveling if the height of the basket, if the height of the basket is 3.5 meters and the height of the basketball player is two meters, that means that the change in the rather this placement in the wind direction is equaling 1.5 meters. Given that the ball needs to travel 1.5 meters above the height of the basketball player in order to reach the basket. And so this would be equaling the lost City initial sign of 40 degrees because we know that the basketball player is throwing the projector during the ball 40 degrees above the horizontal. This would be multiplied by T plus 1/2 multiplied by negative 9.80 meters per second squared multiplied by T squared. And so we can say that we can lose the units at this 0.1 point 05 equaling. We could save the initial T multiplied by sine of 40 degrees, which is approximately 400.64 29 plus rather, buddy at minus 4.9 t squared. And so we can say that toe exes equaling the ex initial t and this is gonna be equaling. Rather recon say 10 meters is gonna be equaling the initial T co sign of 40 degrees. And so we can say that. Then the initial T is gonna be equaling 10 meters divided by co sign of 40 degrees, and this is equaling 13 point 055 meters. And so we're substituting this in for velocity initial t here. And so we have again 1.5 equaling 13.55 times 0.6429 minus 4.9 t squared and then solving for t squared T is gonna be equaling 1.2 to 4 seconds so we can use your 2 84 85 or 89. In order to calculate this, um, you can use your cell function or you can algebraic Lee manipulate. Either way, it's Kurt, but you're going to get the same exact answer. So here it's gonna be This would be the time of flight for the time of flight for the basketball. And at this point, we can simply say that if the initial T is equaling 13.55 we can say that the initial velocity is simply 13.55 meters, divided by 1.2 to 4 seconds, and this is equally 10 0.66 meters per second. Therefore, the initial speed of the basketball must be at least 10 points. Rather should be exactly 10.66 meters per second in order for hit. In order for the basketball to land in the basket without hitting the backboard. That is our final answer here. That is the end of the solution. Thank you for watching

Carnegie Mellon University
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