1. PH 201 Dr. Cecilia Vogel Lecture 4

2. REVIEW  Constant acceleration  x vs t, v vs t, v vs x  Vectors  notation  magnitude and direction OUTLINE  2-D motion with acceleration  Projectiles  acceleration of gravity  Circular motion  constant speed with acceleration

3. Special Case: Projectile Motion  Object moving with no acceleration except that of gravity.  falling object  thrown object  This is 2-D motion, so vector equations stand for  the y- motion is constant accel  a y = -g = -9.8 m/s 2  g is a positive #  the x-motion is constant velocity  a x =0

4. Projectile Motion x-component y-component

5. Projectile motion  x- and y-components are independent an object dropped from rest or projected horizontally both have v yo = 0, both fall in exactly the same way, both hit ground at same time

6. Special Case:  How long will it take a thrown object to reach its max height, h? Given v oy = vo*sin(theta) y i = 0 At max height, v y =0 find t Note – time to go up and back down is twice that

7. Special Case:  How high will thrown object go? v oy = vo*sin(theta) y i = 0 At max height, v y =0, y=h find h Height and time of flight depend only on y-component!

8. Range  Height and time only depend on y-component of initial velocity!!!!!  Range = horizontal distance covered while going up and back down to original height  Range depends on both components  Horizontal motion is constant velocity, so  R= x = v ox t  where t=time up and back down

9. PAL - Range  Three children are playing monkey-in-the-middle. Jeff throws a ball over Joe's head to Jim, who catches the ball at the same height it was thrown from. Joe is 60 cm from Jeff, Jim is 2 m from Jeff. The ball is thrown with an initial speed of 20 m/s. 1.At what angle was the ball thrown? 2.Find the vertical and horizontal components of the initial velocity. 3.At what time did the ball go directly over Joe’s head? 4.How high was the ball (above its thown height) when it went over Joe’s head?