A passenger walks forward along the aisle of a train at a speed of 2.2mi/hr as the train moves along a straight track at a constant speed of 57.5mi/hr with respect to the the ground.

Question

What is the passengers speed with respect to the the ground?

Answer 1

Relative Motion:

Passenger's speed = 2.2 mi/hr relative to the train

Train's speed = 57.5 mi/hr relative to the ground

The problem does not state the direction that the passenger is moving in the aisle so I am going to assume that the passenger is moving in the forward direction, the same as the forward direction of the train.

t = train

g = ground

p = passenger

v_pg = speed of the passenger with respect to the ground

v_pt = speed of the passenger with respect to the train

v_tg = speed of the train with respect to the ground

Using the equation:

v_pg = v_pt + v_tg

(*** Note that the inner "t"s cancel in the subscripts on the right side of the equation resulting in pg)

Substituting in our givens:

v_pg = 2.2 + 57.5 = 59.7 mi/hr FINAL ANSWER