When baseball outfielders throw the ball?

Question

When baseball outfielders throw the ball, they usually allow it to take one bounce on the theory that the ball arrives sooner this way. Suppose that after the bounce the ball rebounds at the same angle as it had when released but loses half its speed.

a. Assuming the ball is always thrown with the same initial speed, at what angle should the ball be thrown in order to go the same distance D with one bounce as one thrown upward at = 46.0° with no bounce?

b. Determine the ratio of the times for the one-bounce and no-bounce throws.
t1b / t0b =

Answer 1

This is an interesting question

For all three flights is found the flight time by first finding the time to apogee
v(t)=v0*sin(th)-g*t
since at apogee v(t)=0
t=v0*sin(th)/g

the total flight time between bounces is 2*t

For the ball that bounces, it has two flights. The first flight has flight time

2*v0*sin(th)/g

and, since the angle is the same, but the speed is v0/2, the time of the second bounce is
v0*sin(th)/g
for a total flight time of
3*v0*sin(th)/g

The ball that flies the total distance has flight time
2*v0*sin(46)/g

so the ratios of time are
t(bounce)/t(fly)=
(3/2)*sin(th)/sin(46)

So we need th, which is the first part of the question anyway.

The distance will be equal.
The distance between bounces is found by plugging t into
x(t)=v0*cos(th)*t

for the bouncing ball, there are two segments
v0*cos(th)*2*v0*sin(th)/g
and
(v0/2)*cos(th)*v0*sin(th)/g
or
D=2.5*v0^2*cos(th)*sin(th)/g

for the single flight
D=v0*cos(46)*2*v0*sin(46)/g
or
D=2*v0^2*cos(46)*sin(46)/g
since the distance is the same
2/2.5=sin(th)*cos(th)/
(sin(46)*cos(46))

solve for th
th=26.5 degrees

so the ratio of the times is
0.93



The bounce is in fact faster.

for a throw from left field inAT&T Park to home, or a distance of 320 feet and a 90 mph throw from the outfielder
90 mph = 132 ft/second
the flight time for the no bounce is
3.49 seconds
and the one bounce is
3.25 seconds.
a diff of 0.24 seconds.

this is significant considering that the average time for a right handed batter to reach first is 4.3 seconds. Although the throw is to home, you get a feel.

j

Answer 2

returned, no diagram. you are able to no longer replica the subject verbatim from the e book and assume to get help. a minimum of attempt to clean up the subject your self and ask particular questions...that's lots much less confusing and greater rewarding than all that typing.