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(II) Vectors $\vec { \mathbf { A } }$ and $\vec { \mathbf { B } }$ are in the $x y$ plane and their scalar product is 20.0 units. If $\vec { \mathbf { A } }$ makes a $27.4 ^ { \circ }$ angle with the $x$ axis and has magnitude $A = 12.0$ units, and $\vec { \mathbf { B } }$ has magnitude $B = 24.0$ units, what can you say about the direction of $\vec { \mathbf { B } } ?$

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$113.4^{\circ}$ or $-58.6^{\circ}\left(301.4^{\circ}\right)$

Physics 101 Mechanics

Chapter 7

Work and Energy

Work

Kinetic Energy

Potential Energy

Energy Conservation

Rutgers, The State University of New Jersey

University of Washington

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University of Sheffield

Lectures

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In physics, the kinetic energy of an object is the energy which it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body in decelerating from its current speed to a state of rest. The kinetic energy of a rotating object is the sum of the kinetic energies of the object's parts.

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7.29. So we have two vectors A and B in the X Y plane. We're told what they're, um what? They're not product, and the respective magnitudes are. We're also told that a makes an angle of 27.4 degrees with the X axis. So now we want what we want to discuss. What can we say about the direction of B? So basically, we know that already the they're, um they're not product is positive, which means that there has to be an acute angle between and be like if we you have a over here and so B could be an acute angle from a either, uh, counterclockwise or clock wives. So we're going to get two possibilities for the direction. Now, from what we know about dot products, you know that a thought e it's going to be the magnitude of a times the magnitude that be finds the coastline of the angle between them. This has to equal 20. No. Now this implies that there's an 86 degree angle between the two factors. So the angle that he makes with the X axis is going to be the angle of that a makes plus or minus this 86 degrees, because so it's either at 113 point four degrees or negative 58 quite six degrees from the excesses.

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