A river flows due east at 1.10 m/s. A boat crosses the river from thesouth shore

Question

A river flows due east at 1.10 m/s. A boat crosses the river from thesouth shore to the north shore by maintaining a constant velocityof 13.0 m/s due northrelative to the water. (a) What is the velocity of the boat relative to shore?
m/s
°(north of east)

(b) If the river is 310 mwide, how far downstream has the boat moved by the time it reachesthe north shore?
m (a) What is the velocity of the boat relative to shore?
m/s
°(north of east)

(b) If the river is 310 mwide, how far downstream has the boat moved by the time it reachesthe north shore?
m

Explanation / Answer

a) for the boat: vx = 1.10 m/s (east) vy = 13.0m/s (north) v =[(vx2+vy2)]=[(1.10m/s)2+ (13.0m/s)2] = 13.05 m/s = tan-1 (vy/vx) =85.16 0 b) since distance dy = 310 m the time take is t = dy / vy = 310m /13.0m/s = 23.85 s dx = vx *t = 1.10m/s*23.85s = 26.24m answer: 26.24m downstream has the boat moved by the time itreaches the north shore b) since distance dy = 310 m the time take is t = dy / vy = 310m /13.0m/s = 23.85 s dx = vx *t = 1.10m/s*23.85s = 26.24m answer: 26.24m downstream has the boat moved by the time itreaches the north shore

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