#6 #14 #20 #22 #24 #286. If you are riding on a merry-go-round, in which directions do your velocity, acceleration, and net force point?
The direction of your velocity is tangent to your circular path. The direction of the change in your velocity, your acceleration, and the force exerted on you to keep you in your circular path are all toward the center of the merry-go-round. The sketch below depicts the direction of your velocity and the force exerted on you at one point on the merry-go-round.
14. Most foot races take places on unbanked tracks. How do the racers turn the corners?
The friction between the bottom of the runner's shoes (or feet if the runner has no shoes) and the track surface provides the force necessary for the runner to turn corners.
20. A quarterback throws a long pass toward the end zone. At the instant the ball reaches its highest point, what are the directions of the ball's velocity, the net force on the ball, and the ball's acceleration?
At the top of the football's trajectory its velocity is strictly horizontal, toward the end zone. If we ignore air resistance, the sole force acting on the ball is gravity. Since the force of gravity acts down, the acceleration is down. (Air resistance would be acting against the direction of the ball's velocity, horizontally away from the end zone.)
22. A hammer dropped on the surface of Mars falls with an acceleration of 3.7 meters per second squared. Would its acceleration be smaller, larger, or the same if it were thrown horizontally at 10 meters per second?
The acceleration of gravity on Mars is the same in each case, so the acceleration of the hammer would be the same.
24. A one-kilogram ball is thrown horizontally with a speed of 20 meters per second. At the same time a two-kilogram ball is thrown horizontally, but with half the speed. Which ball hits the level ground first?
The horizontal and vertical motions are independent. Since the initial vertical velocities of the two are the same, they hit the ground at the same time. (Mass has nothing to do with this problem.)
28. What is the relationship between the directions of the velocity and the acceleration for circular motion at a constant speed?
The velocity and the acceleration are always perpendicular to one another for an object in circular motion. This can be seen in the figure in the response to question 6 above.