Homework Answers

A soccer player kicks a ball at an angle of 37 degree from the horizontal with an initial speed

of 50 ft/sec. Assume that the ball moves in a vertical plane. a) Find the time t1 at which the

ball reaches the highest point of its trajectory. b) How high does the ball go? c) What is the

horizontal range of the ball and how long is it in the air? d) What is the velocity of the ball as

it strikes the ground?

A particle of mass m is attached to the end of a string and moves in a circle of radius of

radius r on a frictionless horizontal table. The string passes through a frictionless hole in the

table and, initially, the other end id fixed. a) if the string is pulled so that the radius of the

circular orbit decreases, how does the angular velocity change if it is ω0 when r = r0? b) what

work is done when the particle is pulled slowly in from a radius r0 to a radius r0/2?

A spaceship of mass m has velocity v in the positive x direction of an inertial reference

frame. A mass dm is fired out the rear of the ship with constant exhaust velocity (-v0) with

respect to the spaceship. a) using conservation of momentum, show that dv/v0 = dm/m, b)

By integration, find the dependence of v on m if v1 and m1 are the initial values. c) Can the

acceleration be constant if dm/dt, the burning rate is constant.