Question

A river 108.4 m wide flows toward the south at 30.5 m/min. A girl on the west bank wishes to reach the east bank in the least possible time. She can swim 108.4 m in still water in 1.60 min.

(a) How long does it take her to cross the river?

(b) How far downstream does she travel?

c) What is her velocity relative to land? Magnitude and direction

(d) What is the total distance she travels?

(e) In what direction must she swim if she wishes to travel straight across the river?

Answer 1

Here is what I solved before, please modify the figures as per your question. Please let me know if you have further questions. Ifthis helps then kindly rate 5-stars.

A river 108.0 m wide flows toward the south at 35.6 m/min. A girl on the west bank wishes to reach the east bank in the least possible time. She can swim 108.0 m in still water in 1.15 min. (a) How long does it take her to cross the river? (b) How far downstream does she travel? (c) What is her velocity relative to land? (c-1) What is the Magnitude? (c-2) What is the direction south of east? (d) What is the total distance she travels? (e) How far must she swim if she wishes to travel straight across the river?   

a) She can do it in 1.95 minutes.
b) (1.96 x 60) = 117 secs. (1.96 x 30.2) = 59.192m. downstream.
c) Her swimming velocity = (100.2/117s), = 0.8564m/sec.
The river's velocity = (30.2/60s) = 0.5033m/sec.
Her velocity relative to the ground = sqrt. (.8564^2 + .5033^2) = 0.993m/sec.
The direction she swims is atn. (.5033/.8564), = 30.45 deg., S of E.
d) Total travel distance = (.993 x 117s) = 116.181m.
e) She will need to angle upstream at 30.45 deg. relative to the west bank, to cross and land directly opposite.