Problem Solving Practice Falling Objects Graphical Analysis “Never play leapfrog with a unicorn.”—Anonymous

Read section 2.6, and solve the worked examples for yourself using the “litany for kinematics.” Don’t look at the solutions until you finish or get stuck! We will practice plenty on this! I’ll work the example from the “litany for kinematics” on the board.litany for kinematics Solving Problems “You are speeding on a city street late at night at 20 m/s. A traffic light turns red, and you slam on your brakes 15 m before the intersection. Your car then slows down at a rate magnitude of 10 m/s 2. How far into the intersection will your car be when it finally comes to a stop?”

You are speeding on a city street late at night at 20 m/s. A traffic light turns red, and you slam on your brakes 15 m before the intersection. Your car then slows down at a rate magnitude of 10 m/s 2. How far into the intersection will your car be when it finally comes to a stop? 1. diagram 3. axes 2. dynamical quantities 4. label positions 5. OSE 7. solve algebraically 6. replace generics 8. solve and box answer

If air resistance can be ignored, falling objects are a special case of uniformly accelerated linear motion. Falling Objects The equations of section 2.5 apply for falling objects. There is no need to write any new equations. You may substitute y for x if you wish.

For objects falling near the surface of the earth, the acceleration is constant and has a magnitude of approximately g=9.8 m/s 2. Note that g is a magnitude! What do you have to do if you want to make g into a vector? For objects falling near the surface of the earth, the acceleration is constant and has a magnitude of approximately g=9.8 m/s 2. (Sometimes I may tell you to use g=10 m/s 2 to simplify calculations). Note that g is a magnitude! What do you have to do if you want to make g into a vector? Will you ever write g=-9.8 m/s 2 ? Note that g is a magnitude! What do you have to do if you want to make g into a vector? Will you ever write g=-9.8 m/s 2 ? Only if you like losing points! y x a=-9.8 m/s 2 y x a=g

(A) Where is the ball after 2 seconds?(A) Where is the ball after 2 seconds? (B) Flip the direction of your axis, and repeat question (A). (A) Where is the ball after 2 seconds? (B) Flip the direction of your axis, and repeat question (A). (C) Is the ball going up the or is it coming down? (A) Where is the ball after 2 seconds? (B) Flip the direction of your axis, and repeat question (A). (C) Is the ball going up the or is it coming down? (D) Where would it be if it were initially thrown downwards at 15 m/s instead of upward? Example: A student stands at the top of a cliff of height 80 m. He throws a ball straight up with initial speed 15 m/s in such a way that it just misses the cliff going down. Assume g = 10 m/s 2. This is the physics 23 “Example of Expert Analysis and Technique in a One-Dimensional Problem” handout.handout

Consider, as an example, free fall (graphics are from hyperphysics). hyperphysics Graphical Analysis of Linear Motion t=0

Example with acceleration changing (but constant over intervals in time).