A batter hits a softball over a third baseman\'s head with speed v 0 and at an a

Question

A batter hits a softball over a third baseman's head with speed v0 and at an angle from the horizontal. Immediately after the ball is hit, the third baseman turns and runs at a constant velocity v=7.000m/s, for a time t=2.000s. He then catches the ball at the same height at which it left the bat. The third baseman was initially l=18.00m from home plate (the location where the ball was hit from). a) Find v0. Use g=9.807m/s2 for the magnitude of the acceleration due to gravity. Assume that there is no air resistance. b) Find the angle in degrees. c)Find the components vx and vy of the ball’s velocity, v, 0.100 s before the ball is caught. d)Find the vector components x and y of the ball’s position, r, 0.100 s before the ball is caught.

Explanation / Answer

a) Let vox and voy are the componenets of Vo.

distance travelled in x-direction, x = vox*T

18 + 2*7 = vox*2

==> vox = 32/2

= 16 m/s

time of flight, T = 2*voy/g

voy = T*g/2

= 2*9.807/2

= 9.807 m/s

so, vo = sqrt(vox^2 + voy^2)

= sqrt(16^2 + 9.807^2)

= 18.77 m/s

b) theta = tan^-1(voy/vox)

= tan^-1(9.807/16)

= 31.5 degrees

c) at t = 1.9 s

vx = vox = 16 m/s

vy = voy - g*t

= 9.807 - 9.807*1.9

= -8.83 m/s

d) x = vox*t

= 16*1.9

= 30.4 m

y = voy*t - 0.5*g*t^2

= 9.807*1.9 - 0.5*9.807*1.9^2

= 0.93 m

r = xi + yj

= 30.4 i + 0.93 j

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