Vector Mechanics for Engineers: Dynamics 10th A volleyball player serves the bal

Question

Vector Mechanics for Engineers: Dynamics 10th

A volleyball player serves the ball with an initial velocity v0 of magnitude 13.40 m/s at an angle of 20degree with the horizontal. Determine (a) if the ball will clear the top of the net, (b) how far from the net the ball will land.

Explanation / Answer

Initial velocity Vo = 13.40 m/s Initial horizontal component Vo_x =13.40*cos(20) = 12.6 m/s Initial vertical component Vo_y =13.40*sin(20) = 4.58 m/s Horizontal distance traveled before net S=9m time taken = t1= S/Vo_x = 9/ 12.6 =0.714 m maximum height reached h=Vo_y^2/(2g) = 4.58^2/(2g) = 1.069 m height from ground (h1)= 1.069+2.1 =3.17 m time taken to reach maximum height (t2) =Vo_y/g = 4.58/9.81 =0.47 s since height of ball at net (h2) = h1-(1/2)*g*(t1-t2)^2 =3.17-0.29=2.88 m therefore h2> 2.43(height of net). So it will cross over (answer) Time taken to land from maximum height to ground (t3) t3 =sqrt(2*h1/g) =0.80 s total time taken by ball to travel (t4)= t2+t3=1.274 s distance traveled by ball =Vo_x*(t4) =12.6*1.274= 16 m distance from net = 16-9 = 7m (answer)

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