A passenger on a boat moving at 1.70 m/s on a still lake walks up a flight of stairs at a speed of 0.60 m/s, as shown in the figure. The stairs are angled at 45° pointing in the direction of motion as shown.
Write the vector velocity of the passenger relative to the water. Express your answer using two significant figures. Express your answer in terms of the unit vectors [tex] \mathbf{i} [/tex] and [tex] \mathbf{j} [/tex].
Answer (2)
The velocity of the **passenger **relative to the water is the sum of the motion due to the boat and the component of the motion up the stairs in horizontal (i) and vertical (j) directions. This gives the vector as (1.70 m/s + 0.60 * 0.71)m/s i + (0.60 * 0.71) m/s j. ;
The vector velocity of the passenger walking up the stairs relative to the water is approximately v passenger = 2.1 i + 0.42 j . This result accounts for the movement of the boat and the passenger's walking direction. The total horizontal component is 2.1 m/s, while the vertical component is 0.42 m/s.
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