This problem deals quantitatively with the experiment of problem 1.1. Let 5 denote the ground frame of reference and 5' the train's rest frame. Let the speed

of the train, as measured by ground observers, be 30 m/sec in the x direction, and

suppose the stone is released at t' = a at the point x' = y' = 0, z' = 7.2 m.

(a) Write the equations that describe the stone's motion in frame 5'. That is,

give x', y', and z' as functions of t'. (Note: A body starting from rest and moving

with constant acceleration g travels a distance 1/2 gt2 in time t. Gravity produces a

constant acceleration whose lnagnitude is approximately 10 m/sec/sec.)

(b) Use the Galilean transform, ation to write the equations that describe the

position of the stone in frame S. Plot the stone's position at intervals of 0.2 sec,

and sketch the curve that describes its trajectory in frame 5. What curve is this?

(c) The velocity acquired by a body starting from rest with acceleration g is gt.

Write the equations that describe the three components of the stone's velocity in

5', and use the Galilean velocity transformation to find the velocity components

in S.

(d) Find the magnitude of the stone's speed at t = 1 sec in each frame.​