3. A boat is propelled at a speed of 4 m/s respect to the water. The boat crosse

Question

3. A boat is propelled at a speed of 4 m/s respect to the water. The boat crosses a stream of water flowing at a constant speed of 1 m/s: the water flows parallel to the river bank whereas the boat aims in a direction perpendicular to the banks as seen by someone on the boat. The width of the river (bank to bank) is 20 m. (i) Calculate the two components of the boat velocity (parallel and perpendicular to the river banks) as seen by someone at rest on the bank of the river. (i) Calculate the speed (i.e. the magnitude of the velocity) of the boat as seen by someone at rest on the bank of the river. (ii) Calculate how long it will take the boat to cross the river.

Explanation / Answer

(i) The perpendicular component is 4m/sec

The parallel component is 1 m/sec

(ii) The speed is sqrt (4^2 + 1^2) = 5 m/sec

(iii) The distance travelled is:

20/distance = cos (theta) = 4/5

distance = 25 m

Time taken = 25/4 = 6.25 secs

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