You are playing right field for the baseball team. Your team is up by one run in the bottom of the last inning of the game when a ground ball slips through the infield and comes straight toward you. As you pick up the ball 62 m from home plate, you see a runner rounding third base and heading for home with the tying run. You throw the ball at an angle of 30° above the horizontal with just the right speed so that the ball is caught by the catcher, standing on home plate, at the same height you threw it. As you release the ball, the runner is 14.0 m from home plate and running full speed at 7.0 m/s.

Question

You are playing right field for the baseball team. Your team is up by one run in the bottom of the last inning of the game when a ground ball slips through the infield and comes straight toward you. As you pick up the ball 62 m from home plate, you see a runner rounding third base and heading for home with the tying run. You throw the ball at an angle of 30° above the horizontal with just the right speed so that the ball is caught by the catcher, standing on home plate, at the same height you threw it. As you release the ball, the runner is 14.0 m from home plate and running full speed at 7.0 m/s. 
Will the ball arrive in time for your team's catcher to make the tag and win the game?

Henry · Answer

Dx = Vo^2*Sin(2A)/g = 62 m.
Vo^2 = *sin60 / 9.8 = 62.
Vo^2*sin60 = 607.6.
Vo^2 = 607.6 / sin60 = 701.6.

Vo = 26.5 m/s @ 30 Deg.
Xo = 26.5cos30 = 22.93 m/s.
Yo = 26.5*sin30 = 13.25 m/s.

Tr = d / Vr = 14m / 7m/s = 2 s. = Time
it takes runner to reach homeplate.

Dx = Xo*T = 62 m.
22.93*T = 62.
T = 62 / 22.93 = 2.7 s. = Time in flight.

No, the runner will arrive 0.7 s ahead
of the ball.