### Projectiles (Biomechanics)

#### Projectiles

Below is a worked example, however see Projectiles from the Kinematics section of the Mechanics page for more examples.

#### Worked Example: Finding the horizontal and vertical components

###### Worked Example

A netball is released at an angle of $65^{\circ}$ with an initial speed of $9 \mathrm{ms^{-1} }$. Find the horizontal and vertical components of the ball's initial velocity.

###### Solution

We can use the sine and cosine relationships in a right angled triangle to calculate the horizontal and vertical components, $v_h$ and $v_v$.

We have that \begin{align} v_h & = 9 \mathrm{ms^{1} } \times \cos 65^{\circ}, \\ & = 3.81 \mathrm{ms^{-1} } \text{ (to 3s.f.).} \end{align} We also have that \begin{align} v_v & = 9 \mathrm{ms^{-1} } \times \sin 65^{\circ}, \\ & = 8.16 \mathrm{ms^{-1} } \text{ (to 3s.f.).} \end{align} The magnitude of the horizontal component is always equal to the magnitude of the initial velocity multiplied by the cosine of the projection angle. In the same way the vertical component is always equal to the magnitude of the initial velocity multiplied by the sine of the projection angle.

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