PHYSICS 103: Lecture 5 Agenda for Today: Review HW Solutions Projectile Motion Example Problems Hitting a target

Horizontal and Vertical Motion are Independent Constant Motion (no acceleration) dhorizontal = d0 + v0t range Acceleration FREE FALL dvertical = v0yt + 1/2at2 height

The horizontal and vertical motions combine to produce the trajectory of the projected ball.

The total velocity at any point is found by adding the vertical component to the horizontal component.

Trajectories for different initial velocities of a ball rolling off a table: v3 is larger than v2, which in turn is larger than v1.

Example: Throwing a ball out from a rooftop What is the distance from the base of the Empire State Building a ball lands if it is thrown horizontally at 20 m/s? What is the final velocity? initial horizontal motion v e r t i c a l m o n final

Example: Throwing a ball out from a rooftop The vertical motion is independent of the horizontal motion. Therefore, the time it takes for the ball to fall in the vertical direction is the limiting time the ball is in the air. Remember from previous class that the time it takes for a ball to fall from the top of the Empire state bldg: t ~ 8.72 s dhorizontal = v0xt = 20 m/s x 8.72 s = 174.4 m ~ 572 ft The final velocity just before impact is the resultant of the velocity in the x- and y-directions. Hence, vfx v2 = vfx2 + vfy2 = (20 m/s)2 + (85.46 m/s)2 Therefore, vfy v v ~ 87.77 m/s

Hitting a Target A target shooter fires at a distant target Hitting a Target A target shooter fires at a distant target. The bullet falls as it travels to the target. Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.

Throwing a Football The flight of a football launched at an angle of 30° to the horizontal. The vertical and horizontal positions of the ball are shown at regular time intervals.

PROJECTILE MOTION Example: Throwing a ball at an angle from a hilltop What is the distance down range from the base of a hill 30 m high if a ball is thrown up at a 50o angle above the horizontal at 40 m/s? What is the time of flight? What is the maximum height? v e r t i c a l m o n y 50o initial final x horizontal motion Range = R

Example: Throwing a ball at an angle from a hilltop To calculate the downrange distance, we need to calculate the time the ball is in the air. The time is determined from vertical (y) motion. v0 v0x v0y 50o v0y = v0 sin50o Once we know the time in the air, we can calculate how far down range it will travel in that amount of time.

Main Points from Today’s Lecture Projectile Motion You should understand that the horizontal and vertical motion for a projectile are independent You should be able to calculate how far down range a projectile will travel if it is thrown at a given speed and angle