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 v_0x = +2.2 m/s anda. The y components of the puck's initial velocity and acceleration are and . Find (a) the magnitude v and (b) the direction ? of the puck's velocity at a time of . Specify the direction relative to the +x axis._x = +7.7 m/s²v_0y = +5.3 m/sa_y = -2.4 m/s²t = 0.50 s.

Answer 1

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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 = +3.0 m/s and ax = +8.7 m/s2. The y components of the puck's initial velocity and acceleration are v0y = +9.2 m/s and ay = -1.7 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.       

Answer

Initial velocity Vo = 3 i + 9.2 j m/s

Acceleration a = 8.7 i - 1.7 j   m/s^2

(a)

Time t = 0.5 s

Final velocity V = Vo + at

                         = (3 i + 9.2 j) + (8.7 i - 1.7 j)(0.5)

                         = 7.35 i + 8.35 j

Magnitude |V| = Sqrt[(7.35)^2 + (8.35)^2]

                       = Sqrt[54.02 + 69.72]

                       = Sqrt[123.74]

                       = 11.12 m/s

(b)

Direction ? = Tan^-1[8.35/7.35]

                 = Tan^-1[1.136]

                 = 48.64 degrees above the + ve X axis