1. An airplane is traveling 715 km/h in a direction 43.5° west of north. (a) Fin

Question

1. An airplane is traveling 715 km/h in a direction 43.5° west of north.

(a) Find the components of the velocity vector in the northerly and westerly directions.

(b) How far north and how far west has the plane traveled after 3.00 h?

km

2. A swimmer is capable of swimming 0.40 m/s in still water.

(a) If she aims her body directly across a 75 m-wide river whose current is 0.45 m/s, how far downstream (from a point opposite her starting point) will she land?
m
(b) How long will it take her to reach the other side?
s

3.A boat can travel 2.20 m/s in still water.

(a) If the boat points its prow directly across a stream whose current is 1.00 m/s, what is the velocity (magnitude and direction) of the boat relative to the shore?
m/s  °
(b) What will be the position of the boat, relative to its point of origin, after 3.00 s? (See the figure above.)

Explanation / Answer

1.

(a) The components of the velocity vector in the northerly and westerly directions.

V(north) = 715 * cos43.5° = 518.64 km/h

V(west)   = 715 * sin43.5 = 492.17 km/h

(b) After time t = 3 h,

d(north) = V(north) * t = 518.64 * 3 = 1555.92 km

d(west) = V(west) * t = 492.17 * 3 = 1476.51 km

2)

(b) The time taken by her to cross the river,

t = d / V(swimmer) = 75 / 0.4 = 187.5 s

(a) The distance covered in downsream direction for this,

d = V(still water) * t = 0.45 * 187.5 = 84.375 m

3)

(a) The velocity of boat will be in two direction, one is along it's own direction and one towards direction of the flow of the river water.

V(BW) = 2.2 m/s

V(WS) = 1 m/s

(b)After time t = 3 s, the position of the boat will be changed with displacement as below directions,

d(displacement downstream) = V(BW) * t = 2.2 * 3 = 6.6 m

d(displacement across the river) = V(WS) * t = 1 * 3 = 3 m

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