A ball is moving through the x-z plane. You can ignore the effects of gravity fo

Question

A ball is moving through the x-z plane. You can ignore the effects of gravity for this problem. At t = 0 s, the ball is at the origin (x = 0 m, z = 0 m) and moving with a velocity vector v? = ( -4.5 x?0 + 3.4 z?0 ) m/s, where x?0 and z?0 are unit vectors in the x and z directions, respectively. The ball hits a wall at thit = 2.3 s and bounces off the wall. After the bounce, the z component of the velocity is reduced by 1/9 of its original value. The x component of the velocity is reversed and its magnitude is reduced to 1/4 of its original value. How far away from the origin is the ball at tfinal = 8 s? At t = 8 s, the ball is d = meters away from the origin.

A ball is moving through the x-z plane. You can ignore the effects of gravity for this problem. At t = 0 s, the ball is at the origin (x = 0 m, z = 0 m) and moving with a velocity vector v? = ( -4.5 x?0 + 3.4 z?0 ) m/s, where x?0 and z?0 are unit vectors in the x and z directions, respectively. The ball hits a wall at thit = 2.3 s and bounces off the wall. After the bounce, the z component of the velocity is reduced by 1/9 of its original value. The x component of the velocity is reversed and its magnitude is reduced to 1/4 of its original value. How far away from the origin is the ball at tfinal = 8 s? At t = 8 s, the ball is d = meters away from the origin.

Explanation / Answer

displacement of ball in z direction
Z = 3.4*2.5 + (3.4/9)*(8-2.3) = 10.3 m
displacement of ball in x direction,
x = (-4.5*2.3) + (4.5/4)*(8-2.3) = -3.94 m
net displace ment = sqrt(z^2+x^2) = 11.02 m from the origin

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