🤓 Based on our data, we think this question is relevant for Professor Perez's class at MEMPHIS.

A dart is thrown horizontally with an initial speed of 10 m/s toward point *P*, the bull’s-eye on a dart board. It hits at point *Q* on the rim, vertically below *P*, 0.19 s later.

(a)What is the distance *PQ*?

(b) How far away from the dart board is the dart released?

This problem asks us to calculate the **vertical** and **horizontal distance** the dart travels, given the **initial velocity** and **time of flight**.

For **projectile motion problems in general**, we'll follow these steps to solve:

- Identify the
and__target variable__for__known variables__—remember that__each direction__*only*(Δ**3**of the**5**variables*x*or Δ*y*,*v*_{0},*v*,_{f}*a*, and*t*)*are needed*for each direction. Also, it always helps to sketch out the problem and label all your known information! __Choose a UAM__—sometimes you'll be able to go directly for the target variable, sometimes another step will be needed in between.**equation**for the target (or intermediate) variable, then**Solve**the equation__substitute known values__and__calculate__the answer.

The four UAM (kinematics) equations are:

$\overline{)\mathbf{}{{\mathbf{v}}}_{{\mathbf{f}}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}{{\mathbf{v}}}_{{\mathbf{0}}}{\mathbf{}}{\mathbf{+}}{\mathbf{a}}{\mathbf{t}}\phantom{\rule{0ex}{0ex}}{\mathbf{\u2206}}{\mathbf{x}}{\mathbf{=}}{\mathbf{}}\mathbf{\left(}\frac{{\mathbf{v}}_{\mathbf{f}}\mathbf{+}{\mathbf{v}}_{\mathbf{0}}}{\mathbf{2}}\mathbf{\right)}{\mathbf{t}}\phantom{\rule{0ex}{0ex}}{\mathbf{\u2206}}{\mathbf{x}}{\mathbf{=}}{\mathbf{}}{{\mathbf{v}}}_{{\mathbf{0}}}{\mathbf{t}}{\mathbf{+}}{\frac{1}{2}}{\mathbf{a}}{{\mathbf{t}}}^{{\mathbf{2}}}\phantom{\rule{0ex}{0ex}}{\mathbf{}}{{{\mathbf{v}}}_{{\mathbf{f}}}}^{{\mathbf{2}}}{\mathbf{=}}{\mathbf{}}{{{\mathbf{v}}}_{{\mathbf{0}}}}^{{\mathbf{2}}}{\mathbf{}}{\mathbf{+}}{\mathbf{2}}{\mathbf{a}}{\mathbf{\u2206}}{\mathbf{x}}}$

We define our coordinate system so that the **+ y-axis is pointing upwards** and the

For a **horizontally launched projectile**, we __also__ know that ** v_{0}_{y} = 0**.

Projectile Motion: Horizontal & Negative Launch

Projectile Motion: Horizontal & Negative Launch

Projectile Motion: Horizontal & Negative Launch

Projectile Motion: Horizontal & Negative Launch

Projectile Motion: Horizontal & Negative Launch