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Problem Set 1 - time t of their contact Show that for...

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Problem Set I. Fall 2006 Physics 200a R. Shankar 1. From the top of a building of height h = 100 m I throw a stone up with velocity 10 m/s . What is the maximum height it reaches and when is that? How many seconds does it spend on its way down between h = 50 m and h = 0 m ? What is its velocity when h = 50 m ? If when it is airborne I quickly dig a hole 50 m deep, when and with what speed will it hit the bottom? 2. Romeo is at x = 0 at t = 0 when he sees Juliet at x = 6 m . (a) He begins to run towards her at v = 5 m/s . She in turn begins to accelerate towards him at a = - 2 m/s 2 . When and where will they cross? Sketch their motions measuring time horizontally and position vertically. (b) Suppose instead she moved away from him with positive acceleration a . Find a max , the maximum a for which he will ever catch up with her. For this case find the
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Unformatted text preview: time t of their contact. Show that for smaller values of a these star crossed lovers will cross twice. Draw a sketch for this case. Explain in words why they cross twice. 3. A particle moves as per the equation x = 30 + 40 t + 60 t 2 + 40 t 3 . Find its velocity and acceleration for all times. When does its velocity equal 1 m/s? At that instant what is its acceleration? 4. [Difficult] Ball A is dropped from rest from a building of height H exactly when ball B is thrown up vertically. When they collide A has double the speed of B . If the collision occurs at height h what is h/H ? Hint: Write equations for heights y A , y B and velocities v A and v B . What can you say about these at the time of the collision?...
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