Looking for the complete answer for Question 3!! 2. A tennis player is viewed fr

Question

Looking for the complete answer for Question 3!!

2. A tennis player is viewed from above with a video camera during a training exercise. The player is instructed to swing a racquet in the horizontal plane with a straight arm as hard as possible at an oncoming tennis ball without any trunk movement (see illustration below). At frame 0, the instant before motion starts, the arm is at an angle of -70° (0o). At frame number 15, just prior to impact with the ball, the arm is at an angle of 30° (015) a) If the video camera has a frame rate of 60 frames/s, and the arm accelerates uniformly during the swing, calculate the angular velocity of the arm just prior to impact. b) If the player has an arm length of 60cm, find the linear velocity of the hand (VT) just prior to impact. just prior to impact. head (110 cm from shoulder) just prior to impact. c) Calculate the tangential and normal acceleration vectors aTH and aNH) at the hand d) Calculate the tangential and normal acceleration vectors (aTR and avR) at the racquet Frame 15:

Explanation / Answer

2.

given, thetao = -70 deg

theta15 = 30 deg

a. given fps = 60

so time taken to reach from thetao to theta15 = 15/60 = 0.25 s

let angular acceleration of the arm be alpha

initial angular speed = 0

final angular speed = w

then

angle rotated = (30 + 70) = 100 deg = 100*pi/180 = 5pi/9 rad

hence

5(pi/9) = 0.5*alpha*t^2 = 0.5*alpha*0.25^2

alpha = 55.8505 rad/s/s

hence

2*alpha*theta = w^2 = 2*55.8505360 * 5pi/9

w = 13.96 rad/s

b. linear velocity = v

arm length l = 0.6 m

v = l*w = 8.377580 m/s

c. tangential accelaration opf hand just before impact, at = alpha*l = 33.5103 m/s/s

radial acceleration, ar = v^2/l = 116.9568 m/s/s

d. at the racquet head

tangential acceleration = at = alpha*1.1 = 61.43555 m/s/s

radial acceleration = w^2*1.1 = 214.36976 m/s/s

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