Question

Consider 2 observers, S and S', who are observing each other and the motion of a particle in their relative frames. They make the following observations at t-0: 1. The particle is located at 50.0 m, 45° relative to S and at (16.0, 12.0) m relative to S'. 2. S' measures the particle to have a velocity of (1.00, 0) m/s 3. S measures S' to have an initial velocity of (-5.00, 0) m/s 4. S measures S' to have a constant acceleration of (-1.00, 0) m/s a) Using an appropriate scale, draw the locations of the S and S' at t-0. b) What is the significance of observation 3? Can we conclude that S is at rest? Why or why not? Justify your answer c) Find the velocity of the particle in the S frame at t-0 and then find the Galilean transformation equations for S. Where is the particle in each frame of reference after 10.0 s? d)

Answer 1

Motion with respect to reference frames with relative velocity and acceleration

Motion with respect to reference frames with relative velocity and acceleration Let the locations of the particle at t = 0 in s and s' frames be r^rightarrow (0) = x(0) i^cap + y(0) j^cap + and r^rightarrow(0) = x'(0) i^cap + y'(0) j^cap, where we assume that the x, x' and y, y' axes are parallel therefore x(0) = 50 cos 45 degree = 50/squareroot 2 m y(0) = 50 sin 45 degree = 50/squareroot 2 m x'(0) = 16 m y'(0) = 12 m Let d^rightarrow = position of s' frame origin with respect to s frame origin Then r^rightarrow = d^rightarrow + r^rightarrow or d^rightarrow = r^rightarrow - r^rightarrow' At t = 0 d^rightarrow(0) = r^rightarrow(0) - r^rightarrow'(0) = {x(0) - x'(0)} i^cap + {y(0) - y'(0)} j^cap = (50/squareroot 2 - 16) i^cap + (50/squareroot 2 - 12) j^cap a) y' = 19.35 i^cap + 23.35 j^cap scale 2 cm congruent 19.35 m portion of s and s' at t = 0