Ch 03: 2D Motion (Projectile Motion)WorksheetSee all chapters
All Chapters
Ch 01: Units & Vectors
Ch 02: 1D Motion (Kinematics)
Ch 03: 2D Motion (Projectile Motion)
Ch 04: Intro to Forces (Dynamics)
Ch 05: Friction, Inclines, Systems
Ch 06: Centripetal Forces & Gravitation
Ch 07: Work & Energy
Ch 08: Conservation of Energy
Ch 09: Momentum & Impulse
Ch 10: Rotational Kinematics
Ch 11: Rotational Inertia & Energy
Ch 12: Torque & Rotational Dynamics
Ch 13: Rotational Equilibrium
Ch 14: Angular Momentum
Ch 15: Periodic Motion (NEW)
Ch 15: Periodic Motion (Oscillations)
Ch 16: Waves & Sound
Ch 17: Fluid Mechanics
Ch 18: Heat and Temperature
Ch 19: Kinetic Theory of Ideal Gasses
Ch 20: The First Law of Thermodynamics
Ch 21: The Second Law of Thermodynamics
Ch 22: Electric Force & Field; Gauss' Law
Ch 23: Electric Potential
Ch 24: Capacitors & Dielectrics
Ch 25: Resistors & DC Circuits
Ch 26: Magnetic Fields and Forces
Ch 27: Sources of Magnetic Field
Ch 28: Induction and Inductance
Ch 29: Alternating Current
Ch 30: Electromagnetic Waves
Ch 31: Geometric Optics
Ch 32: Wave Optics
Ch 34: Special Relativity
Ch 35: Particle-Wave Duality
Ch 36: Atomic Structure
Ch 37: Nuclear Physics
Ch 38: Quantum Mechanics

Concept #1: Intro to Projectile Motion

Example #1: Horizontal Launch

Practice: An object rolls from the top of a hill (shown below) with 20 m/s and takes 4 s to hit the floor. 

(a) Find the object’s range. 

(b) How tall is the hill?

Example #2: Horizontal Launch

Practice: When an object that is launched horizontally hits its target, its velocity has horizontal and vertical components of 80 m/s and 60 m/s, respectively. Find the object’s range.

Practice: In a regulation-sized beer pong table, the ping pong ball is tossed from a horizontal distance of 2.4 meters and 1.0 meter above the top of its target cup. What horizontal speed must you throw the ball with, so it makes the cup?

Example #3: Negative Launch

Practice: You throw an object from the top of a building with 50 m/s directed at 53 o below the horizontal. It covers a horizontal distance of 80 m while in the air. Find its: 

(a) total time of flight.
(b) final velocity (magnitude and direction).

Additional Problems
Two children are playing catch. One throws a ball with an initial velocity of 3 m/s at an angle of 40 degrees with respect to the horizontal. What is the speed of the ball when it reaches its maximum height above the ground? A) 2.3 m/s B) 1.9 m/s C) 0 m/s D) 3 m/s
A projectile is fired from the ground at 50 m/s with a launch angle of 30o. What will the height of the projectile be after 1 s?
A ball is thrown and follows the parabolic path shown. Air friction is negligible. Point Q is the highest point on the path. Points P and R are the same height above the ground. Which of the following diagrams best indicates the direction of the acceleration, if any, on the ball at point P?
A cat chases a mouse across a 0.94 m high table. The mouse steps out of the way, and the cat slides off the table and strikes the floor 1.0 m from the edge of the table. The acceleration of gravity is 9.81 m/s2 . What was the cat’s speed when it slid off the table? 1. 2.42611 2. 2.28431 3. 4.24654 4. 2.24614 5. 3.58982 6. 4.09007 7. 5.63425 8. 3.49639 9. 2.75587 10. 7.44296
A man throws a rock from a height of 10 m above the ground with an intial speed of 10 m/s at an angle of 30° above the horizontal. Use g = 10m/s2. [a] Find the maximum height above the man reached by the rock. [b] Find the time elapsed when it hits the ground. [c] Find the horizontal distance traveled by the rock to the point where it strikes the ground. [d] Find the magnitude of the velocity of the rock just as it strikes the ground.
Given: The battleship and enemy ships A and B lie along a straight line. Neglect air friction. A battleship simultaneously fires two shells (with the same muzzle velocity) at these two enemy ships. If the shells follow the parabolic trajectories shown in the figure, which ship gets hit first? 1. need more information 2. B 3. A 4. both at the same time
A cannon is placed on a tower an UNKNOWN height h from the ground. The cannon is inclined an angle α from the horizontal when a ball is fired. Assuming that there is no friction, that the initial speed of the ball is v0, and that the ball lands a distance L from the base of the tower: a) How high above ground does the ball go? b) What is the speed of the ball at the maximum height? c) What is the height h of the tower? If needed, you can assume you know h for parts (a) and (b). Write your results in terms of α, v  0, L, g, and h (only for parts a and b). Remember to check the dimensions/units for each answer.
At the highest point on the trajectory of a particle moving in projectile motion, which quantity below is equal to zero? A) the speed of the particle B) the acceleration of the particle C) the vertical component of the velocity D) the horizontal component of the velocity
Consider the setup of a gun aimed at a target (such as a monkey) as shown in the figure. The target is to be dropped from the point A at t = 0, the same moment as the gun is fired. The bullet hits the target at a point P. Let the initial speed of the bullet be v0 = 108 m/s, let the angle between the vector v0 and the horizontal (x) direction be θ = 50.9° and let AB = 90.2 m. The distance d = OB is the x-coordinate of the target. The acceleration of gravity is 9.8 m/s2 . The height BP where the collision takes place is
A projectile is launched through the air at 20 m/s with a launch angle of 65 o. At what height will the projectile have lost 50% of its speed?
An NFL quarterback will often throw lobs at 20 m/s with a launch angle of 50  o. If a wide receiver runs away from the quarterback at a speed of 7 m/s, how long should the quarterback hold onto the football before throwing it, so the receiver can catch it without slowing down? Assume that the throw and the catch occur at the same height.
Given: The battleship and enemy ships 1 and 2 lie along a straight line. Neglect air friction. Consider the motion of the two projectiles fired at t = 0. Their initial speeds are different and they reach different maximum heights h1 and h2. What is the ratio of the time of flight, t 1 and t2 respectively, that the shells reach?1. t1 / t2 = 2 (√ h1 / h2)2. t1 / t2 = 1/ √2 (√ h1 / h2)3. t1 / t2 = 2 (√ h2 / h1)4. t1 / t2 = 1/2 (√ h1 / h2)5. t1 / t2 = (√ h1 / h2)6. t1 / t2 = 1/2 (√ h2 / h1)7. t1 / t2 = h2 / h18. t1 / t2 = √2 (√ h1 / h2)9. t1 / t2 = (√ h2 / h1)10. t1 / t2 = (h1 / h2)
A projectile is launched at an angle of 45 o. If the projectile takes 2 s to reach half its maximum height, what is the launch speed of the projectile?
You’re trying to design a simple catapult, which is capable of firing a projectile at 50 m/s at a launch angle of 45o. If the height of the projectile is 2 m when fired from the catapult, how far will the projectile travel over flat ground?
The speed of an arrow fired from a compound bow is about 37 m/s. An archer sits astride his horse and launches an arrow into the air, elevating the bow at an angle of 51° above the horizontal and 1.3 m above the ground. The acceleration of gravity is 9.81 m/s2 .  What is the arrow’s range? Assume: The ground is level. Ignore air resistance. 1. 137.547 2. 309.949 3. 194.879 4. 26.029 5. 249.356 6. 230.822 7. 25.4438 8. 481.262 9. 203.317 10. 537.785
A small rock is projected from the ground with velocity with magnitude v0 and direction 53.1° above the horizontal. A tall building is a horizontal distance of 26.0 m from where the rock was launched. The rock strikes the building 2.00 s after being launched. Neglect air resistance and assume the ground is level. At what vertical height above the ground does the rock strike the building?
A kid on his bycicle can reach a speed of 15 m/s. If he was able to launch off a 2 m tall ramp at an angle of 45o, how far away from the edge of the ramp would the kid land?