Projectile Motion or Two Dimensional Kinematics

SP1. Students will analyze the relationships between force, mass, gravity, and the motion of objects.b. Compare and contrast scalar and vector quantities. f. Measure and calculate two-dimensional motion (projectile) by using component vectors.Projectile Motion orTwo Dimensional KinematicsWhat is a projectile?Aprojectileis any object that is cast, fired, flung, heaved, hurled, pitched, tossed, or thrown. (Thisisan informaldefinition.)The path of a projectile is called itstrajectory.When a projectile moves horizontally with constant velocity while being accelerated vertically, the result is parabolic motion. How is projectile motion 2-D?Projectile motion is a combination of horizontal motion and vertical motion. The horizontal motion of a projectile is constant because no gravitational force acts horizontally.The vertical motion of a projectile is nothing more than free fall with a constant downward acceleration due to gravity.

Horizontal Launch

Vertical Launch

Does launch velocity matter?

Does launch velocity matter?

Projectile SimulatorCheck Your UnderstandingSuppose a snowmobile is equipped with aflare launcher which is capable of launchinga sphere vertically.

If the snowmobile is in motion, launches the flare, and maintains a constant horizontal velocity after the launch, where will the flare land (neglect air resistance)?

Suppose an airplane drops a flare while itis moving at constant horizontal speed atan elevated height. Assuming that air resistance is negligible, where will the flare land relative to the plane?

A. Directly below the plane. B. Below the plane and ahead of it. C. Below plane and behind it.Check Your Understanding

Why does the horizontal component of aprojectiles motion remain constant?Because no force acts on it horizontally.

Why does the vertical component of a projectiles motion undergo change?Because gravity is pulling it downward.

How does the vertical distance a projectilefalls below an otherwise straight-line pathcompare with the vertical distance it wouldfall from rest in the same time?The vertical and horizontal distances are equal.

A projectile is launched vertically at 100 m/s. If air resistance can be neglected, at what speed does it return to its initial level?100 m/s

Solving projectile problemsHorizontal (x) ComponentSince there is NO acceleration in the x-direction, any equation with a cannot be used, leaving us withvx = x / t

Solving projectile problemsVertical (y) ComponentSince there IS acceleration in the y-direction, any equation with a (really g) can be usedvfy = viy + gty = viyt + gt2vfy2 = viy2 + 2gy

Ex 1: A student sits on the roof of her house which is 12 m high. She can launch water balloons from a slingshot at 25 m/s. If she fires a water balloon directly horizontally:a. How long will it be airborne?b. How far will it travel?c. How fast is the balloon falling vertically?

18Ex 2: A bullet traveling 800 m/s horizontally hits a target 180 m away. How fast is the bullet falling vertically?How far does the bullet fall before it hits the target?How long does it take to hit the target?

20Ex 3: A ball is thrown horizontally from the roof of a building 50 m tall and lands 45 m from the base.How long does it take to hit the ground?How fast is the ball falling vertically?What was the balls initial speed?22Ex 4: A person kicks a rock off a cliff horizontally with a speed of 20 m/s. It takes 7.0 seconds to hit the ground.What is the height of the cliff?What is the final vertical velocity?What is the range of the projectile?24Ex 5: A golfer practicing on a range with an elevated tee 4.9 m above the fairway is able to strike a ball with a horizontal velocity of 20 m/s.a. How long will the ball take to land? b. How far will the ball travel before landing? c. What is the acceleration of the ball 0.5 s after being hit? d. Calculate the speed of the ball 0.80 s after it leaves the club. e. With what speed will the ball hit the ground?

26