🤓 Based on our data, we think this question is relevant for Professor Griffith's class at MC MARICOPA.

Sand moves without slipping at 6.0 m/s down a conveyer that is tilted at 15°. The sand enters a pipe *h* = 3.6 m below the end of the conveyer belt, as shown in the figure:

What is the horizontal distance *d* between the conveyer belt and the pipe?

This problem is asking us to find the **horizontal distance traveled** by the grains of sand given the **magnitude and direction** of the **initial velocity** and the **height** they fall.

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

- Identify the
and__target variable__for each direction—remember that__known variables__*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:

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

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

For projectiles with a** negative launch angle**, we __also__ need to know how to decompose a velocity vector into its *x*- and *y*-components:

$\overline{)\begin{array}{rcl}{v}_{0x}& {=}& \left|{\stackrel{\rightharpoonup}{v}}_{0}\right|\mathrm{cos}\theta \\ {v}_{0y}& {=}& \left|{\stackrel{\rightharpoonup}{v}}_{0}\right|\mathrm{sin}\theta \end{array}}$

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