# A soccer ball is kicked at an angle of 30 to the horizontal with an initial velocity of 16 m/s....

## Question:

A soccer ball is kicked at an angle of 30 to the horizontal with an initial velocity of 16 m/s. How far does the soccer ball go?

A. 3.8 m

B. 6.6 m

C. 13.3 m

D. 22.6 m

## Projectile motion:

An object subject only to the acceleration due to gravity is said to be in projectile motion. The kinematic equations and derivations from them are useful in describing the motion of such objects.

Known Values

• Initial velocity = {eq}v = 16\ m/s {/eq}
• Angle = {eq}\theta = 30^\circ {/eq}
• Acceleration due to gravity = {eq}g = -9.8\ m/s^2 {/eq}
• Range {eq}R {/eq}

Calculations

The range of a projectile can be found by {eq}R = \dfrac{v^2sin(2\theta)}{-g} {/eq}.

{eq}\begin{align} R &= \dfrac{v^2sin(2\theta)}{-g}\\ &= \dfrac{(16\ m/s)^2sin(2(30^\circ))}{(9.8\ m/s^2)}\\ &= 22.6\ m \end{align} {/eq}

This means the soccer ball will go {eq}\boxed{D. 22.6\ m} {/eq}