An outfielder throws a baseball to his catcher in an attempt to throw out a runner at home plate. The ball bounces once before reaching the catcher. Assume the angle at which the bounced ball leaves the ground is the same as the angle at which the outfielder threw it as shown in the figure, but that the ball's speed after the bounce is one-half of what it was before the bounce. 0 O 0 (a) Assuming the ball is always thrown with the same initial speed, at what angle should the fielder throw the ball to make it go the same distance D with one bounce (blue path) as a ball thrown upward at 45.0° with no bounce (green path)? (b) Determine the ratio of the time interval for the one-bounce throw to the flight time for the no-bounce throw. tone-bounce tno-bounce

When baseball players throw the ball from the out eld, they usually allow it to take one bounce before it reaches the in eld because they think that the ball will arrive sooner that way. Suppose that the angle at which a bounced ball leaves the ground is the same as the angle at which it is thrown but the ball's speed after the bounce is one-half of what it was just before the bounce. (a) Assume that the ball is always thrown with the same initial speed. At what angle  should the elder throw the ball to make it go the same distance D with one bounce as a ball thrown upwards at 45  with no bounce? (b) Determine the ratio of the time intervals for the two paths. Is it better to throw the ball on a bounce?

Water in a river flows with a component downstream (x-direction) of 6 m/s and a component across the stream (y-direction) of 4 m/s. A boat is attempting to cross the river. The velocity of the boat relative to the water is 20 m/s at an angle of 70 degrees with respect to the x-axis. Determine the velocity of the boat relative to the shore.

Professional golfers can drive the ball over 200 m. While air resistance is significant, its effects are nearly canceled because lift is gained from backspin on the ball, and so a reasonable description of the ball’s trajectory is obtained if air resistance is neglected. Suppose a golfer hits a ball 200 m on level ground, giving it an initial velocity at an angle of 45o. The duration of the impact of the club and ball has been measured to be 1.00 ms. c) Find the average force exerted by the club on the ball. d) Find the average shear deformation of the club's 0.800 m long and 1.00 cm diameter steel shaft.