Problem

Measuring $g .$ One way to measure $g$ on another…

03:10

Problem 51 Hard Difficulty

(. A tennis ball on Mars, where the acceleration due to gravity is 0.379$g$ and air resistance is negligible, is hit directly upward and returns to the same level 8.5 s later. (a) How high above its original point did the ball go? (b) How fast was it moving just after being hit? (c) Sketch clear graphs of the ball's vertical position, vertical velocity, and vertical acceleration as functions of time while it's in the Martian air.

Answer

$v_{0}=15.7854 \mathrm{m} / \mathrm{s}$
$y_{1}=100.6316 \mathrm{m}$
See Graph.

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Physics 101 Mechanics

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Video Transcript

So this problem in laws who article motions, Let's take positive. Why, Toby? Upward on DH. Positive x to do what's right now When the when the ball is thrown up. Why now? The new treatise to maximum height. It comes to rest for the moment. So the final velocity for this Ah, for the, uh, poor travel is cereal. And then after the second, it drops ended. So for this particular tragic deliver, the ball is travelling off. Word going aboard. So we have Levi. Is Siegel the initial velocity off the board? I meant that it's thrown upward is 3.71 Meet up a second now. Sorry, this is the acceleration. This is the acceleration. That is 3.71 Neat oppa seconds. Good. But the fact still addition is down one. So there should be a negative sign because we have taken our positive by access Toby upward. So acceleration points in the negative I axis, and therefore it should have a negative sign. Now, time is going to be 4.25 seconds. Now, if you consider the motion for the maximum height backto the initial eval. So this particular case so for this. The final velocity off the upward motion becomes the initial velocity for the downward motion. Because when the ball moves upward and reaches the maximum height, the velocity become zero. So for this particular tragic story followed by the ball, the final velocities you. Now it stays there for a moment and then force down drops back. So this velocity becomes the initial velocity for this tragic Really? So when the ball ah, drugs from the maximum height back to the initial level, we have the not white on Aceto. Let's mark this like this and for the skills It's mark this like this for this er prisons off one motion and this represents downward motion. Now time is the same for 0.25 seconds. Now we find ah, distance covered by the boy. So we will lose the secretion over here. So we have this job going to seal on DH. You saw this using the wrist off the perimeters. We have thiss gives y minus. Why not to the equal Go negative 33 point five meters. So the height off side of the ball went 33.5 meters of off religion and tradition Now, for part B one was going to AA take from here is why not is the initial height And why is the final light? So then the boy drops back Why not this? Actually this height that is not Sedona and this is the final light. So this is zero because the ball falls to the ground ultimately. So why is zero on this means that hi, Dr Ball is why not minus life. And if you put that in this a question you see that height is 33.5 meters How high the walls Because from its original position. So this is positive. So our calculation makes sense Now For the second part, consider the motion from just after it was hit to the maximum height. So basically the blue area. So for that we have the right to be called CDO. We have time before 0.5 seconds to same. Now we need to find the initial velocity with which the ball wass Solidum brick the ball. The ball was thrown upward. So we have the video's dis equation on DH. From here, we will get with not why is negative off a righty And if you solve it, using the values you giving, you get the initial velocity dated with 15.8 meters per second. So this is the velocity with which the ball was thrown from the ground over the last part. So we know that acceleration is constant on is downward now, since we took positive. Why, Toby, off words acceleration this negative but is a constant. So the blocked off acceleration worse esteem will be like this on this value will be negative 3.71 on acceleration in units of meters. A second now for velocity was this time. So you fuel use this equation. You'll see that velocity is a linear function ofthe time but keeps on decreasing because final velocity is zero and initial velocity is some positive. This means that a lot should start from here on. Will finally come to see Leo in XX, sis, that time is we're going to five seconds. On this valley was the initial velocity which we found Toby 15.8 meters per second. This is the college in his country. Let me just It is thiss five because it looks like my thing. Uh, okay, I'm writing the coordinates. At this point, it is very we should Smartly light is physically access. Now for the last block, it is distance. So we have live our Sistine. Let's take this to the origin for this. Let's fall of this a question. So we see that. Oh, let me just for goddess squared over here. But the calculations are good. So we see that, uh, distances a quadratic, uh, function off. Yeah, this means that a motion with the quantity, But for this case Yeah, why not? For the pirin downward motion by not is some positive value. And why is CEO so? Ah, just a minute. So, yes, so basically reveal plot using the whole voter, considering both of these two cases. So the ball travels upward and then stays there for the second. Renard's velocity become CEO, and then Dobbs back. So this equations let's say the ball starts from here. It is. Uh, it is close enough to zero nonsecure. Exactly. So this will be This is basically why not hand go up and then come down following a quadratic are falling a parabolic part because depends on time quantity. Kly on. This is basically Why not less that if you take wine on Toby zero so the ball is thrown from the ground. You're, uh this plant will shift up off up to here, but it's better to droid this May because we're holding the ball. Someone is willing. The ball on DH er that person's height comes into account for the initial height off the ball, so why not? Is Ah, when you are drawing grabs, it's better to not take my not to be content zero.

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