Ch 03: 2D Motion (Projectile Motion)WorksheetSee all chapters
 Ch 01: Units & Vectors 2hrs & 22mins 0% complete Worksheet Ch 02: 1D Motion (Kinematics) 3hrs & 11mins 0% complete Worksheet Ch 03: 2D Motion (Projectile Motion) 3hrs & 8mins 0% complete Worksheet Ch 04: Intro to Forces (Dynamics) 3hrs & 42mins 0% complete Worksheet Ch 05: Friction, Inclines, Systems 4hrs & 32mins 0% complete Worksheet Ch 06: Centripetal Forces & Gravitation 3hrs & 51mins 0% complete Worksheet Ch 07: Work & Energy 3hrs & 55mins 0% complete Worksheet Ch 08: Conservation of Energy 6hrs & 54mins 0% complete Worksheet Ch 09: Momentum & Impulse 5hrs & 35mins 0% complete Worksheet Ch 10: Rotational Kinematics 3hrs & 4mins 0% complete Worksheet Ch 11: Rotational Inertia & Energy 7hrs & 7mins 0% complete Worksheet Ch 12: Torque & Rotational Dynamics 2hrs & 9mins 0% complete Worksheet Ch 13: Rotational Equilibrium 4hrs & 10mins 0% complete Worksheet Ch 14: Angular Momentum 3hrs & 6mins 0% complete Worksheet Ch 15: Periodic Motion (NEW) 2hrs & 17mins 0% complete Worksheet Ch 15: Periodic Motion (Oscillations) 3hrs & 16mins 0% complete Worksheet Ch 16: Waves & Sound 3hrs & 25mins 0% complete Worksheet Ch 17: Fluid Mechanics 4hrs & 39mins 0% complete Worksheet Ch 18: Heat and Temperature 4hrs & 9mins 0% complete Worksheet Ch 19: Kinetic Theory of Ideal Gasses 1hr & 40mins 0% complete Worksheet Ch 20: The First Law of Thermodynamics 1hr & 49mins 0% complete Worksheet Ch 21: The Second Law of Thermodynamics 4hrs & 56mins 0% complete Worksheet Ch 22: Electric Force & Field; Gauss' Law 3hrs & 32mins 0% complete Worksheet Ch 23: Electric Potential 1hr & 55mins 0% complete Worksheet Ch 24: Capacitors & Dielectrics 2hrs & 2mins 0% complete Worksheet Ch 25: Resistors & DC Circuits 3hrs & 20mins 0% complete Worksheet Ch 26: Magnetic Fields and Forces 2hrs & 25mins 0% complete Worksheet Ch 27: Sources of Magnetic Field 2hrs & 30mins 0% complete Worksheet Ch 28: Induction and Inductance 3hrs & 38mins 0% complete Worksheet Ch 29: Alternating Current 2hrs & 37mins 0% complete Worksheet Ch 30: Electromagnetic Waves 1hr & 12mins 0% complete Worksheet Ch 31: Geometric Optics 3hrs 0% complete Worksheet Ch 32: Wave Optics 1hr & 15mins 0% complete Worksheet Ch 34: Special Relativity 2hrs & 10mins 0% complete Worksheet Ch 35: Particle-Wave Duality Not available yet Ch 36: Atomic Structure Not available yet Ch 37: Nuclear Physics Not available yet Ch 38: Quantum Mechanics Not available yet

## Projectile Motion: Positive Launch

See all sections
Sections
Intro to 2D Motion
Projectile Motion
More Projectile Motion
Initial Velocity in Projectile Motion
Circular Motion

# Solution: 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 fr

###### Problem

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?

###### Solution

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:

1. Identify the target variable and known variables for each direction—remember that only 3 of the 5 variablesx or Δy, v0, vf, a, and t) are needed for each direction. Also, it always helps to sketch out the problem and label all your known information!
2. Choose a UAM equation—sometimes you'll be able to go directly for the target variable, sometimes another step will be needed in between.
3. Solve the equation for the target (or intermediate) variable, then substitute known values and calculate the answer.

The four UAM (kinematics) equations are:

In our coordinate system, the +y-axis is pointing upwards and the +x-direction is horizontal along the launch direction. That means ay = −g, and ax = 0 (because the only acceleration acting on a projectile once it's launched is gravity.)

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

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

$\overline{)\mathbf{|}\stackrel{\mathbf{⇀}}{\mathbit{v}}\mathbf{|}{\mathbf{=}}\sqrt{{{\mathbit{v}}_{\mathbit{x}}}^{\mathbf{2}}\mathbf{+}{{\mathbit{v}}_{\mathbit{y}}}^{\mathbf{2}}}}$

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