A rookie quarterback throws a football with an initial upward velocity component of 12.0 m/s and a horizontal velocity component of 20.0 m/s. Ignore air resistance. (c) How much time (after it is thrown) is required for the football to return to its original level? How does this compare with the time calculated in part (a)?

Video transcript

welcome back everybody. We are throwing an orange and we are told that it has an initial vertical velocity of 50 m/s and we are told that its initial horizontal velocity is around half of that of 25 m/s. So we have that its initial velocity is represented by this vector right here. Now it is going to follow projectile motion, meaning it will have an arc of something like this. Where at the top of this point you're going to have your maximum height. And we are asked to find how much time it takes to get to this end point right here. Well, if we're looking at this parabola, if we kind of draw a line down the center, you can see by cemetery that the time to get to this maximum height is going to be the same time to get from the maximum height back down to the bottom again. So you can say that the time that we're looking for is two times the time it takes to get to the maximum height. Now, since we are dealing with projectile motion, we can also say that To find the time to reach our maximum height. This is just going to be our initial vertical velocity over our gravitational vertical acceleration. I say gravitational because in projectile motion, the only acceleration acting on that object is going to be the acceleration due to gravity which is about 9.8 m/s square. So let's go ahead and plug in our values to this function right here, we have t max is equal to our initial vertical velocity of 50 divided by our gravitational acceleration of 9.8, which is equal to 5.10 seconds. Now to find T. We do two times R. T. Max, which is two times 5.10 equal to 10.20 seconds corresponding to our answer choice of D. Thank you guys so much for watching. Hope this video helped, and we will see you all in the next one.