4 Recap: Acceleration due to Gravity (Free Fall) In the absence of air resistance all objects fall with the same constant acceleration of about g = 9.8 m/s2near the Earth’s surface.
5 Recap: Example2 m5 m/sA ball is thrown upwards at 5 m/s, relative to the ground, from a height of 2 m.We need to choose a coordinate system.
6 Recap: Example Let’s measure v0 = 5 m/s time from when y0 = 2 mv0 = 5 m/syLet’s measuretime from whenthe ball is launched.This defines t = 0.Let’s choose y = 0 to be ground leveland up to be the positive y direction.
7 Recap: Example y0 = 2 m v0 = 5 m/s y 1. How high above the ground will the ball reach?usewith a = –gand v = 0.
8 Recap: Example y0 = 2 m v0 = 5 m/s y 2. How long does it take the ball toreach the ground?Usewith a = –gand y = 0.
9 Recap: Example y0 = 2 m v0 = 5 m/s y 3. At what speed does the ball hitthe ground?Usewith a = –gand y = 0.
20 Unit Vectors From the components, Ax, Ay, and Az, of a vector, we can compute its length, A, usingIf the vector A is multipliedby the scalar 1/A we get a newvector of unit length in thesame direction as vector A;that is, we get a unit vector.
21 Unit Vectors It is convenient to define unit vectors parallel to the x, y and zaxes, respectively.Then, we can write avector A as follows:
26 Relative Motion N S W E Velocity of plane relative to air Velocity of airrelative to groundVelocity of planerelative to ground
27 Example – Relative Motion SWEA pilot wants to fly plane due northAirspeed: km/hWindspeed: 90 km/hdirection: W to E1. Flight heading?2. Groundspeed?Coordinate system: î points fromwest to east and ĵ points from south to north.
44 Uniform Circular Motion Magnitudes of velocityand centripetalacceleration arerelatedas follows
45 Uniform Circular Motion Magnitude of velocityand period T related asfollowsr
46 SummaryIn general, acceleration changes both the magnitude and direction of the velocity.Projectile motion results from the acceleration due to gravity.In uniform circular motion, the acceleration is centripetal and has constant magnitude v2/r.
47 How to Shoot a Monkey H x = 50 m h = 10 m H = 12 m Compute minimum initialvelocityH