For this problem, we're looking for the **launch height** and **final speed** of the golf ball given the **magnitude and ****direction** of the initial velocity and the **horizontal distance** it has to travel.

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:

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

In our coordinate system, the **+ y-axis is pointing upwards** and the

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

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

And the equations to find the magnitude and direction of a velocity from the components:

$\overline{)\mathbf{\left|}\stackrel{\mathbf{\rightharpoonup}}{\mathit{v}}\mathbf{\right|}{\mathbf{=}}\sqrt{{{\mathit{v}}_{\mathit{x}}}^{\mathbf{2}}\mathbf{+}{{\mathit{v}}_{\mathit{y}}}^{\mathbf{2}}}}$

$\overline{){\mathbf{tan}}{\mathbf{}}{\mathit{\theta}}{\mathbf{=}}\frac{{\mathit{v}}_{\mathit{y}}}{{\mathit{v}}_{\mathit{x}}}}$

A golfer tees off from the top of a rise, giving the golf ball an initial velocity of 43.0 m/s at an angle of 30.0° above the horizontal. The ball strikes the fairway a horizontal distance of 180 m from the tee. Assume the fairway is level. (a) How high is the rise above the fairway? (b) What is the speed of the ball as it strikes the fairway?

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: Positive Launch concept. If you need more Projectile Motion: Positive Launch practice, you can also practice Projectile Motion: Positive Launch practice problems.

What professor is this problem relevant for?

Based on our data, we think this problem is relevant for Professor Efthimiou's class at UCF.

What textbook is this problem found in?

Our data indicates that this problem or a close variation was asked in Fundamentals of Physics - Halliday Calc 10th Edition. You can also practice Fundamentals of Physics - Halliday Calc 10th Edition practice problems.