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A physics book slides off a horizontal tabletop with a speed of 1.10 $\mathrm{m} / \mathrm{s}$ . It strikes the floor in 0.350 s. Ignore air resistance. Find (a) the height of the tabletop above the floor, (b) the horizontal distance from the edge of the table to the point where the book strikes the floor, and (c) the horizontal and vertical components of the book's velocity, and the magnitude and direction of its velocity, just before the book reaches the floor.

a) 0.6 $\mathrm{m}$b) 0.385 $\mathrm{m}$c) $72.2^{\circ}$

Physics 101 Mechanics

Chapter 3

Motion in a Plane

Physics Basics

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

Cornell University

Hope College

University of Winnipeg

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So here we have Ah projectile being shot off with the horizontal velocity. We have the ex initial. We know that this equals V X Final because there is no acceleration and the ex direction this will equal 1.10 meters per second. We also know that the projectile is in the air for 0.350 seconds. So in order, find the height that the projectile was fired from. We can say that the auto y equals V y initial t plus 1/2 g t squared Using the kinetic equation, we know that the Y initial equals zero because the projectile has no initial why velocity And this will equal 1/2 times 9.8 times 0.35 squared. And this is equally 0.600 meters. Now Part B is asking us for the horizontal displacement during this delta T, This is an equal v X initial t plus 1/2 a T squared again. There isn't any acceleration in the ex direction. So this goes to zero and we find that this is 1.1 times point 35 and we're getting a 0.385 meters for the horizontal displacement. Now Part C is asking us for the components of the final velocity the magnitude of the final velocity as well as the direction So we can say that B y final equals V Y initial plus GT. We know the view initial equals zero. So we can say that the final Y velocity equals 9.8 times point 35 and we're getting 3.43 meters per second downwards. And so we Khun, we know that the final velocity and the ex direction equals 1.10 meters per second. So we can say that the magnitude of the final velocity is going to be equal to the sum of the squares, the square root of the sum of the squares. So essentially a 3.43 squared plus 1.1 squared all to the 1/2 power and this is giving us 3.60 meters per second. So this is your magnitude of your final philosophy, and we know that data is going to be equal to our 10 of the white component divided by the ex component. So there'll be 3.43 divided by 1.1 and we're getting 72.2 degrees and again because it is falling downwards. This is going to be below positive ex access or below the horizontal. That is the end of the solution. Thank you for watching.

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