Assume all speeds are constant. a) A man walks up a stalled escalator in time t

Question

Assume all speeds are constant.

a) A man walks up a stalled escalator in time tw = 88.3 s. If he stands on the moving escalator, he reaches to top in time tm = 23.0 s. Find twm, the time it would take him to reach the top if he walked up the moving escalator?
t = 1 s

b) A plane flies at speed vstill = 204 km/h in still air. Now, there is a wind blowing at speed vw = 65.8 km/h, with its direction at 49.4 degrees to the east of north. If the pilot wishes to fly due north with the wind blowing, find:
- the angle between the direction the plane flies and due north: ? = 2 degrees
- the speed at which the plane will fly relative to the ground: vp = 3 km/h

Explanation / Answer

suppose v = man's velocity and u = escalator's velocity d/v = 88.3 v = d/88.3 d/u =23 u = d/23 d/(u+v)= 18.24 s 204 sin theta = 65.8 cos49.4 theta = 12.117 degrees v= 204 cos 12.117 + 65.8 sin 49.4 = 249.42 km/h

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