Coursehero >> Connecticut >> Yale >> PHYS 200

Course Hero has millions of student submitted documents similar to the one below including study guides, homework solutions, papers, exam answer keys and textbook solutions.

Physics 1 200a PSII 1. Let A = 3i + 4j and B = 5i - 6j. (i) Find A + B, A - B, 2A + 3B, and C such that A + B + C = 0. (ii) Find A , the length of A and the angle it makes with the x-axis. 2. A train is moving with velocity vT G = 3i + 4j relative to the ground. A bullet is fired in the train with velocity vBT = 15i - 6j relative to the train. What is the bullets' velocity vBG relative to the ground? 3. Consider the primed axis rotated relative to the unprimed by an angle in the counterclockwise direction. (i) Derive the relation Ax = Ax cos - Ay sin Ay = Ay cos + Ay sin that expresses unprimed components in terms of primed components of a vector A using class notes if needed to get started. (ii) Invert these relations to express the primed components in terms of unprimed components. In doing this remember that the sines and cosines are constants and that we should treat Ax and Ay as unknowns written in terms of knowns Ax and Ay . (Thus multiply one equation by something, another by something else, add and subtract etc to isolate the unknowns. Use simple trig identities) (iii) Argue why one could have obtained this result easily by reversing . (iv) Consider a specific case Ax = 1, Ay = 1, = /4. What do you expect for Ax and Ay based on a sketch? Confirm by explicit calculation. (v) Verify that the length squared of A comes out same in both systems. 2 (Vi) Consider another vector B and its components in the two frames. Show that AxBx + Ay By = AxBx + Ay By . We will understand this invariance later. 4. A particle is located at r(t) = 14ti + 6t2j. Find its position, velocity and acceleration at t = 2 s. 5. At a wedding the 2m tall bride throws her bouquet with a velocity v0 = 25m/s an at angle 370 above the horizontal. It is caught by a friend of height 1.5m. How long is the bouquet in flight and how far did it go horizontally? What was its maximum height above the ground? 6. Estimate the acceleration of the moon towards the earth given it orbits it once in 28 days at a radius of about a quarter of a million miles. (I know the units are funny and numbers are approximate. This problem tests your ability to give a quick and decent estimate, say to 10 percent .) 7. A jet pilot diving vertically down at 600 km/hr wants to make a quarter turn without experiencing an acceleration bigger than 5g. At what height must the turn begin? Assume that the speed is constant and that after the quarter turn the plane, moving horizontally, is at ground level. 8. Here is problem designed so people in the life sciences will feel physics is relevant to them. A monkey is hanging from a height h and a person d meters away from the tree and on the ground, wants to zap it (in today's version with a tranquilizer gun and in the original version, a hunting rifle). He aims straight at the monkey and fires. This would of course work in the absence of gravity but show that it will work even in its presence provided the initial speed obeys v0 > (d2 + h2)g/2h) What does this requirement ensure? Given 3 that this will also work if a pulse of laser light is used, what do you learn about light in a gravitational field? People interested in other areas can replace monkey by suitable object, e.g., hard drive or a copy of Kant's Critique of Pure Reason. 9. Show that if a projectile is shot from a height h with speed v0 the v0 . maximum range obtains for for launch angle = ArcT an 2 2gh+v0

Find millions of documents here - Study Guides, Homework Solutions, Papers, Exam Answer Keys and more. Course Hero has millions of course related materials that will enable you to learn better, faster and get an A in all your courses.
Below is a small sample set of documents: