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:

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

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?

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Projectile Motion: Horizontal & Negative Launch concept. If you need more Projectile Motion: Horizontal & Negative Launch practice, you can also practice Projectile Motion: Horizontal & Negative Launch practice problems.

What professor is this problem relevant for?

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