AP Physics 1 - Understanding Vector and Scalar Quantities

A ball is thrown at a velocity of $12\frac{m}{s}$ at an angle of from the horizontal. What are the ball's horizontal and vertical velocities?

Ball_32_degrees

$v_y=6.36\frac{m}{s}\ \textup{and}\ v_x=10.18\frac{m}{s}$

$v_y=10.18\frac{m}{s}\ \textup{and}\ v_x=6.36\frac{m}{s}$

$v_y=1.26\frac{m}{s}\ \textup{and}\ v_x=3.97\frac{m}{s}$

$v_y=3.97\frac{m}{s}\ \textup{and}\ v_x=1.26\frac{m}{s}$

There is not enough information to solve this problem

Explanation

The velocity of $12\frac{m}{s}$ can be broken into horizontal and vertical components by using trigonometry. Think of the figure below, where x and y velocity components of the total velocity are shown.

Ball_32_degrees_xy

Use the total velocity, the x-component, and the y-component to form a right triangle below.

Xy_velocities

Treating $12\frac{m}{s}$ as the hypotenuse, x-component as the leg adjacent, and y-component as the leg opposite, you can conclude that the velocities are related through trigonometric identities.

$v_y=v\sin\theta$

$v_x=v\cos\theta$

Plugging in the given values, we can solve for the x and y velocity components.

$v_y=(12\frac{m}{s})\sin(32^o)=6.36\frac{m}{s}$

$v_x=(12\frac{m}{s})\cos(32^o)=10.18\frac{m}{s}$

Which answer choice below includes only scalar quantities?

Distance, speed, time

Displacement, time, acceleration

Velocity, displacement, force

Acceleration, energy, displacement

Force, time, velocity

Explanation

Scalar quantities are those that can be described with magnitude only, as opposed to vectors, which include both magnitude and direction components. Distance, speed, and time are all scalars. Displacement is not a scalar, as it involves both the distance and the direction moved from a starting point. Velocity also includes a direction component, and is therefore a vector quantity.

Understanding Vector and Scalar Quantities

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