2D and Relative Motion. Group Problem 02 PROBLEM 1. Against the Grain

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1 PROBLEM 1. Against the Grain You are on the west bank of a river which flows due south and you need to swim to the east bank. You have told your friends to meet you on the east bank directly opposite your starting point. Before starting out you realize that, since the river is flowing swiftly at a speed of 12 ft/s and since your fastest swimming speed in still water is only 5 ft/s, you will inevitably be carried downstream. Nevertheless, you want to minimize the effort expended by your friends in walking downstream to meet you. The width of the river you are to swim across is 300 ft. After a quick calculation, you call over to your friends by cell phone and tell them to start walking to a new meeting point. How far downstream of the original meeting point should you tell them to walk?

2 PROBLEM 2. Escape from a Burning Building Your friend, an expert long jumper, is trapped at the top ledge of a burning building. His only escape route is to jump to the roof of the next building. He calls you to ask for your advice on how to proceed. He thinks his best option is to try jumping to the next building. You happen to know that the next building is 10.0 m away horizontally and its roof is 3.0 m below the ledge on which your friend is standing. You also know that your friend s best long-jump on level ground is 7.9 m. In this jump he can actually manage a take off angle of 45.0 from horizontal. Will he make it to the other side?

3 PROBLEM 3: The star quarterback of the local university says he can run at 6 m/s and, while running, throw the football with a speed of 20 m/s. (All stated values are accurate to 1% and let g = 10 m/s 2 ) (A) The quarterback, at the 50 yard line, and running directly towards the intended receiver directly downfield chooses to throw the football such that, from his perspective, it leaves his arm at an angle 45 above the horizontal. How fast is the ball initially travelling in the vertical direction? In the horizontal direction? (B) How far will it travel before it reaches the receiver (who is at the same height as the quarterback)? (C) In regards to the football s initial velocity, what angle from horizontal will a stationary fan at the 50 yard line observe (as opposed to the 45 above the horizontal in part A)?

4 (D) The execution of the play is problematic and one of the offensive linemen lets a defensive tackle through and he a barreling down on the quarterback (along the line between the quarterback and the receiver) at 6 m/s. When the tackle is one meter from the quarterback he lifts his arms up one meter above the level at which the football is simultaneously released. Will the ball clear the defensive tackle s hands? (E) Can the quarterback readjust his release and still get the ball to the receiver (who is standing stationary and is wide open)? Why or why not? Simply state how you would approach this problem.

5 PROBLEM 4: A car drives at constant speed in a counterclockwise sense around a level (horizontal) track as shown. (A) Pick any three points in different parts of the track and draw the velocity vector of the car at each point. (B) Indicate places on the track where the car s acceleration is zero. (C) Indicate the places where the car s acceleration has its maximum magnitude. (D) Is there ever a tangential component to the acceleration? Why or why not? Track as seen from above. Problem 5: SimCoaster, the Real Thing

6 Amusement parks are great fun and the venerable Tilt-a-Whirl is a perennial favorite. You are asked to examine a new prototype model with a little more whirl. General guidelines suggest a maximum of 3.5 g s on any ride. The general layout of the machine which rotates horizontally is sketched below and the design firm claims to have done its homework. The distance between pivots (A to B or B to C) is 20.0 m and the individual tangential velocities of the two armatures are 6.0 and 2.5 m/s respectively when the ride is operating a full power. The distance from the C pivot to the seat is set to 5 m. Does this new design satisfy the guidelines? (a) What is the radial acceleration at point C? (b) Considering only the rotation about point C, what is the radial acceleration at point D? (c) How does one combine these two accelerations considering that they are vectors? What is the maximum combined acceleration? Where does this happen? (d) How does this compare to v 2 /R where v is the tangential velocity and R is the distance from B to D.