Review: motion with constant acceleration

1. Review: motion with constant acceleration Acceleration: change in velocity / time interval • a = 0 case •  no acceleration  velocity is constant  v = vo •  position vs. time  x = x o + vo t, xo is the starting position 2. acceleration = a = constant velocity v = vo + a t, vo is the initial velocity at time t = 0 s position if motion starts at xo = 0, with vo = 0 (initially at rest)  x = ½ a t2 if the motion is free-fall, then a = g = 10 m/s2.(Note: for text problems use g = 9.8 m/s2)

2. Position, y H • Maximum height Time, t ttop 0 2ttop • Time to highest point Velocity, v v0 Time, t • Total time in air v0 Review: Free fall- object projected vertically up

3. example • An object is dropped from rest from a height of 20 m above the ground.(a) How long will it take to reach the ground? (b) How fast will it be moving when it hits the ground? • Solution: initial velocity, v0 = 0 y = ½ g t2, v = g t

4. L-5 Projectile motion A projectile is an object that is thrown or struck or shot and then travels under the influence of gravity

5. Tennis ball Golf ball Football Softball Soccer ball bullet Hockey puck or ball Basketball Volleyball Arrow Shot put Javelin Projectile Examples These are all examples of things that are projected, then go off under the influence of gravity

6. Not projectiles • Jet plane • Rocket • Car (unless it looses contact with ground) • catapult (before rock leaves) • slingshot (before rock leaves sling)

7. Unintended projectile

8. force of gravity Projectile motion  The key to understanding projectile motion is to realize that gravity acts vertically  gravity affects only the vertical motion, not the horizontal motion

9. Demonstration • We can see that the horizontal and vertical motions are independent • The red ball falls vertically • The yellow ball was given a kick to the right. • They track each other vertically step for step and hit the ground at the same time

10. Galileo’s inclined plane experiments NO! YES

11. Target practice In the absence of gravity a bullet would follow a straight line forever. With gravity it FALLS AWAY from that straight line!

12. Hitting the target – aim high, not directly at the target

13. Football Life without gravity

14. Field goals would be easier to make!

15. Basketball – no jump shots! With gravity

16. v Vertical velocity Horizontal velocity Path of the Projectile: parabola falling rising Height g v Distance downfield (range) projectile

17. Projectile motion – key points-1 • The projectile has both a vertical and horizontal component of velocity • The only force acting on the projectile once it is shot is gravity (neglecting air resistance) • At all times the acceleration of the projectile is g = 10 m/s2downward • The horizontal velocity of the projectile does not change throughout the path

18. Key points-2 • On the rising portion of the path gravity causes the vertical component of velocity to get smaller and smaller • At the very top of the path the vertical component of velocity is ZERO • On the falling portion of the path the vertical velocity increases

19. key points-3 • If the projectile lands at the same elevation as its starting point it will have the same vertical SPEED as it began with • The time it takes to get to the top of its path is the same as the time to get from the top back to the ground. • The range of the projectile (where it lands) depends on its initial speed and angle of elevation

20. 65° y 45° 25° x 15° Maximum Range • When an artillery shell is fired the initial speed of the projectile depends on the explosive charge – this cannot be changed • The only control you have is over the angle of elevation. • You can control the range (where it lands) by changing the angle of elevation • To get maximum range set the angle to 45°

21. The ultimate projectile: putting an object into orbit NEWTON • Imagine trying to throw a rock aroundthe world. • If you give it a large • horizontal velocity, • it will go into orbit • around the earth!