A physics book slides off a horizontal tabletop with a speed of 1...

Question

A physics book slides off a horizontal tabletop with a speed of 1.10 m/s. It strikes the floor in 0.480 s. Ignore air resistance. Find (a) the height of the tabletop above the floor;

Accepted Answer

Welcome back everybody. We have a horizontal board that is above the ground. And we are told that on top of this horizontal board is a metallic sphere. Now this metallic sphere is going to be pushed off of this horizontal board, at which it is going to start to fall to the ground. Following projectile motion. Now we are told a couple of things about this action here, we are told that the ball leaves the board with a horizontal velocity of 2.5 m per second. We're also told during this time that it takes 0.582 seconds to reach the bottom. Now, since we are dealing with projectile motion, we're going to have a vertical acceleration which is the acceleration due to gravity of negative 9.8. And then we also know something about its vertical initial velocity. We're told that its initial horizontal velocity is 2.5, but it's not gonna start dropping down until it is off this cliff. As a result its initial vertical velocity is going to be zero. Now we are tasked with finding what is the height of the board from the ground. Well, our height is going to be equal to the absolute value to the change in y. Just as a little check for us later on, since we are going from a higher place to a lower place, our delta Y is going to be negative. So, let's look out for that. Well, with all of these values, this points me to using our Kinnah Matic equation. So I'm gonna use this one that are delta Y. Is equal to our initial vertical velocity times time plus one half times are vertical acceleration times our time squared We have all these values. So let's go ahead and plug them in Delta Y. Is going to be equal to our initial velocity of zero times our time of 0.582 Plus 1/2 times acceleration due to gravity negative 9.8 times 0.582 Squared. Now this first term is just gonna cancel out because anything times 00 and when you plug the second term into the calculator you get negative 1.66 m. It's good that our answer is negative. That's exactly what we're looking for. So now let's take the absolute value of our delta Y. Absolute value of negative 1.66 is equal to our height of 1. m corresponding to our answer choice of C. Thank you guys so much for watching. Hope this video helped. We will see you all in the next one

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