The figure shows a 0.3 kg baseball just before and just after it collides with a
ID: 2041232 • Letter: T
Question
The figure shows a 0.3 kg baseball just before and just after it collides with a bat. Just before, the ball has velocity V1 of magnitude 12.3 m/s and angle , 31.40. Just after, it is traveling directly upward with velocity 2 of magnitude 9.90 m/s. The duration of the collision is 2.60 ms. What are the (a) magnitude and (b) direction (relative to the positive direction of the x axis) of the impulse on the ball from the bat? What are the (c) magnitude and (d) direction of the average force on the ball from the bat? (a) Number (b) Number (c) Number (d) Number Units Units UnitsExplanation / Answer
mass of the baseball, m=0.3 kg
before collision,
velocity of the ball, v1=12.3 m/sec
theta=31.4 degrees
after collision,
velocity of the ball, v2=9.9 m/sec
duration time, t=2.6*10^-3 sec
a)
along x direction,
impulse, Px=m*(v2x-v1x)
Px=m*(0-(-v1*cos(theta)
Px=m*v1*cos(theta)
Px=0.3*12.3*cos(31.4)
px=3.149 kg.m/sec
along y direction,
impulse, Py=m*(v2y-v1y)
Py=m*(v2-(-v1cos(theta))
Py=0.3*(9.9+12.3*sin(31.4))
Py=4.892 kg.m/sec
magnitude of impulse, dp=sqrt(px^2 + py^2)
=sqrt(3.149^2 + 4.892^2)
=5.82 kg.m/sec
b)
direction, tan(theta)=py/px
tan(theta)=4.892/3.149
===> theta=57.23 degrees w r to x axis
c)
average force, Favg=dP/dt
=5.82/(2.6*10^-3)
=2238.46 N
d)
direction,
theta=57.23 degrees w r to x axis