The figure shows a 0.3 kg baseball just before and just after it collides with a
ID: 1369370 • 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 v 1 of magnitude 13.4 m/s and angle = 31.5degrees . Just after, it is traveling directly upward with velocity v 2 of magnitude 11.9 m/s. The duration of the collision is 2.30 ms. What are the magnitude and direction (relative to the positive direction of the x axis) of the impulse on the ball from the bat? What are the magnitude and direction of the average force on the ball from the bat?Explanation / Answer
here,
v1 = 13.4 m/s and theta = 31.5 degree
v1 = 13.4 * ( cos(31.5 ) i + sin(31.5) j)
v1 = 11.43 m/s i + 7 m/s j
v2 = 11.9 m/s j
mass of the ball , m = 0.3 kg
(a)
impulse = final momentum - initial momentum
impulse = m* ( 11.9 m/s j - 11.43 m/s i - 7 m/s j)
impulse = 1.47 j m/s - 11.43 m/s i
the magnitude of the impulse , |I| = sqrt( 1.47^2 + 11.43^2)
|I| = 11.52 kg . m/s
(b)
theta = arctan( 1.47/11.42)
theta = 7.33 degree
theta is 172.67 degree from the +x axis in counetr clockwise direction
(c)
trhe average force , F = I/t
F = 11.52/0.0023
F = 5008.6 N
the magnitude of the average force needed is 5008.6 N
(d)
direction of average force theta is 172.67 degree from the +x axis in counetr clockwise direction