Posted by **Mariya** on Saturday, March 9, 2013 at 10:04pm.

A boat sets off perpendicular to the bank, to cross a river width of 250m. The speed of the boat in still water is 3.20ms-1, however there is a current downstream at 1.20ms-1, which puss the boat sideways.

a) Find the resultant velocity of the boat.

b) Find the total distance the boat travels in crossing the river.

c) How long does the crossing take?

d) How far downstream from the starting point does the boat travel?

- Physics -
**bobpursley**, Saturday, March 9, 2013 at 10:07pm
a. add the two velocities as vectors.

find the angle of travel down stream

b. distance downstream: you have the angle, and the distance across

c. time=250m/3.20m/s

d. distance downstream=timeinwater/1.20

- Physics -
**Mariya**, Saturday, March 9, 2013 at 10:23pm
thanks. the answers to b. is 167m and the answer to d. is 93.7 m. but I'm not sure how to get that. would you please care to explain how to get that?

- Physics -
**bobpursley**, Saturday, March 9, 2013 at 11:55pm
b. angle: arctan 1.2/3.2

then distance downstreem=250/cosangle

I get for the angle...0.359radians

then for distance = 250/cos.259=259m

Your answer is not possible.

Now another way: time to get across=250/3.2=78.1sec

distance downstream=78.1*1.2=93.7m

now distance total=sqrt(93.7^2+250^2) which is greater than your answer also.

your answer to b is wrong.

- Physics -
**Henry**, Sunday, May 24, 2015 at 8:50pm
a. Vb + Vc = 3.2i + 1.2 = 3.42m/s[69.4o]

= 3.42m/s[20.6o] E. of N.

b. d = 250/Cos20.6 = 267 m.

c. d = V*t = 267 m

3.42*t = 267

t = 78.1 s.

d. d = 250*Tan20.6 = 94 m

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