Braving blizzard conditions on the planet Hoth, Luke Skywalker sets out at top speed in his snowspeeder for a rebel base 4800 mi away. He travels into a steady head wind and makes the trip in 3 hr. Returning, he finds that the trip back, still at top speed but now with a tailwind, takes only 2 hr. Find the top speed of Luke's snow speeder and the speed of the wind.

v_top = 2400 mi/hr

v_w = 400 mi/h

Step-by-step explanation:

Given:

- Total distance D = 4800 mi

- Headwind journey time taken t_up= 3 hr

- Tailwind journey time taken t_down = 2 hr

Find:

Find the top speed of Luke's snow speeder and the speed of the wind.

Solution:

- The speed of Luke v_l is in stationary frame is given by:

                           v_l = v_w + v_l/w

Where,

           v_w: Wind speed

           v_l/w: Luke speed relative to wind.

- The top speed is attained on his returned journey with tail wind. We will use distance time relationship to calculate as follows:

                         v_top = D / t_down

                         v_top = 4800 / 2

                        v_top = v_down = 2400 mi/hr

- Similarly his speed on his journey up with head wind was v_up:

                         v_up = D / t_up

                         v_up = 4800 / 3

                        v_up = 1600 mi/hr    

- Now use the frame relations to find the wind speed v_w:

                         v_down = v_w + v_l/w

                         v_up = -v_w + v_l/w    

- Solve equations simultaneously:

                         2400 =  v_w + v_l/w

                         1600 =  -v_w + v_l/w

                         4000 = 2*v_l/w

                         v_l/w = 2000 mi/h

                         v_w = 400 mi/h