Week 4 Homework Assignment

1. (P.134 Prob.4) The pilot of a small place finds that the airport where he intended to land is fogged in. He flies 55 miles west to another airport to find that conditions there are too icy for him to land. He flied 25 miles south and is finally able to land at the third airport. (a How far and in what direction must he fly the next day to go directly to his original destination? (b) How many extra miles beyond his original flight plan has he flown?
2. (P.135 Prob.12) Vector b has magnitude 7.1 and direction 14° below the +x-axis. Vector c has x-component c_x = -1.8 and y-component  c_y = -6.7. Compare (a) the x- and y-components of b; (b) the magnitude and direction of c; (c) the magnitude and direction of c + b; (d) the x- and y-component of c - b.
3. (P.136 Prob.20) A pulley is hung from the ceiling by a rope. A block of mass M is suspended by another rope that passes over the pu7lley and is attached to the wall ( Fig.4.38). The rope fastened to the wall makes a right angle with the wall. Neglect the masses of the rope and the pulley7. Find (a) the tension in the rope from which the pulley hangs and (b) the angle q  that the rope males with the ceiling.
   
4. (P.137 Prob.32) At t = 0, an automobile traveling north begins to make a turn. It follows one-quarter of the arc of a circle of radius 10.0m until, at t = 1.60s, it is traveling east. The car does not alter its speed during the turn. Find (a) the car's speed, (b) the change in its velocity during the turn, and (c) its average acceleration during the turn.
5. (P.137 Prob.40) Two ballplayers are practicing how to catch fly balls. One stand by home plate and hits balls into the air for the other., some distance away, to catch. A ball is hit with an initial velocity of 22.0m/s at an angle of 60.0° above the horizontal. (a) How high will the ball rise? (b) How much time will elapse from the time the ball leaves the bat until it reaches the fielder? (c) At what distance from home plate will the fielder be when he catches the ball?
6. (P.138 Prob.52)A 6.0-kg block, starting from rest, slides down a frictionless incline of length 2.0m. When it arrives at the bottom of the incline, its speed is v_t. At what distance from the top of the incline is the speed of the block 1/2v_t?
7.  (P. 139 Prob.64) A boy is attempting to swim directly across a river; he is able to swim at a speed of 0.500m/s relative to the water. The river is 25.0m wide and the boy ends up at 50.0m downstream from his start point. (How fast is the current flowing in the river? (b) What is the speed of the boy relative to a friend standing on the riverbank?
8. (p.140 Prob.80) A particle has a constant acceleration of 5.0m/s² to the east. At time t = 0, it is 2.0m east of the origin and its velocity is 20m/s north. What are the components of its position vector at t =2.0s?