Answer to Question #105594 in Mechanics | Relativity for Olawale

Question #105594
In frame S, a particle passes through the origin at time t=0 with a constant velocity U=5m/s making an angle €=tan-1(3/4) with x-axis. Find the position of the particle at time t=2s.Assume another frame S’ which is moving relative to S with velocity V=1m/s x. Find the speed of the particle and its location at time t=2s in frame S’
Expert's answer

The angle of the velocity relative to the x-axis is atan(3/4). Therefore, in 2 seconds, the x-coordinate of the particle will be

"x_2^S=v\\text{ cos}\\bigg(\\text{atan}\\frac{3}{4}\\bigg)t=8\\text{ m}."

If the frame S' moves with a speed of 1 m/s along the x-axis of S to the right, the x-coordinate will be

"x_2^{S'}=\\bigg[v\\text{ cos}\\bigg(\\text{atan}\\frac{3}{4}\\bigg)-u\\bigg]t=6\\text{ m}."

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