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Multiple-Concept Example 4 deals with a situation similar to that presented here. A marble is thrown horizontally with a speed of 15 m/s from the top of a building. When it strikes the ground, the marble has a velocity that makes an angle of 65 with the horizontal. From what height above the ground was the marble thrown?

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Physics 101 Mechanics

Chapter 3

Kinematics in Two Dimensions

Motion in 2d or 3d

Cornell University

University of Washington

Simon Fraser University

University of Winnipeg

Lectures

04:01

2D kinematics is the study of the movement of an object in two dimensions, usually in a Cartesian coordinate system. The study of the movement of an object in only one dimension is called 1D kinematics. The study of the movement of an object in three dimensions is called 3D kinematics.

10:12

A vector is a mathematical entity that has a magnitude (or length) and direction. The vector is represented by a line segment with a definite beginning, direction, and magnitude. Vectors are added by adding their respective components, and multiplied by a scalar (or a number) to scale the vector.

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Multiple-Concept Example 4…

04:03

07:08

04:39

A marble is thrown as a pr…

01:28

02:31

A ball is thrown horizonta…

03:57

A rock climber throws a sm…

02:53

Consult Multiple-Concept E…

The perspective provided b…

01:54

02:42

REFERING TO EXAMPLE 4-9 (a…

So the problem states that a marble is thrown off the top of building at 15 meters per second. And our test is find, um, how high this marble was thrown from were also given the information that once the marble hits the ground, the angle that the velocity vector makes with the horizontal is 65 degrees. So we know for a fact that the horizontal component of the lost is going to stay constant. So this all right here will be 15 meters per second, always, even when it's hitting the ground. Um and we're trying to find what this vertical component is of the velocity because if we do that, we'll be able to find the height. So to do this, we can take the tangent of 65 degrees, which is opposite over adjacent, so that equal the V said why over 15 meters per second, This means visa. Why will be equal to 32.17 meters per second? Now that we know this, we can use our cinematics formula which states that the velocity, the final velocity is equal to the initial velocity. Both of these air squared plus two times the acceleration times the change in displacement which we're trying to find. So we know that the final velocity, of course, is 32.17 meters per second. We're going to square that we also know that the initial velocity in the vertical direction is going to be zero, because the ball, the marvelous turn horizontally. Then we know the acceleration is going to be 9.8 meters per second squared and we're trying to find this displacement. And when we saw for it, we find that Delta X, the height at which the marvel started at, is equal to 52.79 meters.

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