A puck is moving on an air hockey table. Relative to an x , y coordinate system

Question

A puck is moving on an air hockey table. Relative to an x, y coordinate system at time t = 0 s, the x components of the puck's initial velocity and acceleration are v0x = +8.9 m/s and ax = +9.4 m/s2. The y components of the puck's initial velocity and acceleration are v0y = +7.1 m/s and ay = -5.8 m/s2. Find (a) the magnitude v and (b) the direction ? of the puck's velocity at a time of t = 0.50 s. Specify the direction relative to the +x axis.

Explanation / Answer

Vox = 8.9

ax = 9.4

Voy = 7.1

ay - -5.8

Vx = Vox + a*t = 8.9 + 9.4*0.50 = 13.6 m/s

Vy = Voy + a*t = 7.1 + (-5.8)*0.50 = 4.2 m/s

v = (Vx2 + Vy2)1/2 = (13.62 + 4.22)1/2 = 14.23 m/s

Theta = tan-1 (Vy/Vx) = tan-1 (4.2/13.6) = 17.16 degreees above the x axis

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