A physics student on Planet Exidor throws a ball, and it follows the parabolic trajectory shown in FIGURE EX4.13. The ball's position is shown at 1 s intervals until t = 3s. At t = 1s, the ball's velocity is v = (2.0 i + 2.0 j) m/s. (b) What is the value of g on Planet Exidor?

Video transcript

Hey, everyone in this problem, we're told that an animation series designed for Children comprises of a scene that shows aliens playing catch. And we're given a figure that shows the path of the ball and its location. In case we have the exposition of meters on the X axis, the y position of meters on the Y axis. We're told that at time T equals two seconds, the ball has a velocity of 3.55 plus four J meters per second. And we're asked to determine the value of acceleration due to gravity on this imaginary planet. We have four answer choices, options A through D all in meters per second squared. Option A is four. Option B is 7.5. Option C is 3.5 and option D is five point looking at our diagram. OK? We have the velocity given at two seconds. And if we look at three seconds, we can see that this is at the peak of our motion and this is at the maximum physician, maximum height. And we know that when we're at the maximum height, the velocity is going to be zero. So let's think about moving from this point at two seconds to this point at three. So from two seconds to three seconds when we have, well, we have to consider both the extraction in the White Ocean. So in the X direction, we have a velocity of 3.5 m per second. And that's gonna be consistent, we're gonna assume that there is no horizontal acceleration like we typically do with kinematic problems. And so we just have this consistent velocity of 3.5 m per second in the extraction. Does the X that change an X position? We don't know. And we know that the time elapsed is one, had to go from two seconds to three seconds. It takes one second. Now, in the one direction, our initial velocity is gonna be the Y velocity at two seconds and that's gonna be 4 m per second. OK. The J component of the velocity we were given, we also know the final velocity is going to be 0 m per second. And I mentioned that because we're at this maximum height that vertical velocity is going to be zero momentarily as the ball goes from going upwards to coming back downwards. OK. As it switches the acceleration A Y is what we want to find. The time it takes is 16. If we look at all of this information, we can see that in the Y direction we have three known values, one thing we're trying to find and with three known values. That's enough to use our kinematic or U AM equations. So we're gonna choose the equation with the four variables listed here. We're gonna substitute in our values and we're gonna solve. And that equation is vfy is equal to V not Y plus A Y multiplied by T substituting in our value is 0 m per second. The S equal to 4 m per second. What's the acceleration? A Y multiplied by one sec. If we move our 4 m per second to the left-hand side, by subtracting, we end up with A Y is equal to negative m per second squared. OK. After dividing by this one second, so we have our acceleration here A Y which is negative 4 m per second squared. If we look at our answer traces, they're all positive that the question is asking for the acceleration due to gravity. OK? And when we talk about acceleration due to gravity, we always take the positive value and we say that the acceleration A Y is gonna be the negative of our acceleration due to gravity G. OK? And so G is just going to be equal to m per second squared. So comparing to our answer choice, we can see that this corresponds with option A thanks everyone for watching. I hope this video helped see you in the next one.