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 = +3.2 m/s and ax = +1.9 m/s2. The y components of the puck's initial velocity and acceleration are v0y = +8.1 m/s and ay = -6.2 m/s2. Find (a) the magnitude v and (b) the direction θ of the puck's velocity at a time of t = 0.50 s. Specify the direction relative to the +x axis.

Answer 1

X = Xo + a*t
X = 3.2 + 1.9*0.5 = 4.15 m/s^2

Y = Yo + a*t
Y = 8.1 - 6.2*0.5 = 5 m/s.

a. V^2 = X^2 + Y^2
V^2 = (4.15)^2 + 5^2 = 42.2
V = 6.5 m/s.

b. tan A = Y/X = 5/4.15 = 1.20482
A = 50.31o = Direction.

Answer 2

Correction: X = 4.15 m/s.