A river 95.9 m wide flows toward the south at 37.3 m/min. A girl on the west ban

Question

A river 95.9 m wide flows toward the south at 37.3 m/min. A girl on the west bank wishes to reach the east bank in the least possible time. She can swim 95.9 m in still water in 1.85 min.

a) how far downstream does she travel? The answer given was 69 m . How did they get this answer? (please show steps)

b) what is her velocity relative to land? give direction in degrees ( the answer given was 63.9 m/min with a direction of 35.7 degrees south of east) How? (please show steps)

c) what is the total distance she travels (answer given was 118 m) How?

d) In what direction must she swim if she wishes to travel straight across the river? (answer given is 46 degrees) How do i get these answers?


I ask How do i get these answers cuz this is a sample proble with answers but i dont know the steps. Once you give me the steps I can follow with the actual assignment since ur steps will help me understand where these answers come from.

Thank You

c) what is her total distance she travels

Explanation / Answer

a.

The rivers velocity is 37.3[m/min]. Since it takes the girl 1.85[min] to cross the lake, then the distance downstream is:

x=v*t=37.3*1.8569[m/sec]

b.

The girls average velocity in still water is: v=x/t=95.9/1.8551.838[m/min]

she also has a south bound velocity of 37.3[m/min] so in total the magnitude of the velocity is:

|v|=sqrt(37.32+51.8382)63.863[m/min]

and the angle is: =arctan(-37.3/51.838)=-35.74o from the east direction.

c.

the total distance is the distance she traveled east and the distance she traveled south:

x=sqrt(95.92+692)118.143[m]

d.

in order for her to swin in a straight line, she must swin at such an angle that her northern element wil cancel out the river:

meaning 51.838*sin=37.3

=arcsin(37.3/51.838)=46.02o

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