# Sarah can paddle a rowboat at 6 m/s in still water. She heads out across a 400 m river at an angle of 30 upstream. She reaches the other bank of the river 200 m downstream from the direct opposite point from where she started. Determine the river current?

##### 1 Answer

May 27, 2018

Let us consider this as a projectile problem where there is no acceleration.

Let

- Across the river.
- Along the river.

Both are orthogonal to each other and therefore can be treated independently. - Given is width of river
#=400\ m# - Point of landing on the other bank
#200\ m# downstream from the direct opposite point of start. - We know that time taken to paddle directly across must be equal to time taken to travel
#200\ m# downstream parallel to the current. Let it be equal to#t# .

Setting up equation across the river

#(6 cos30)t=400#

#=>t=400/(6 cos30)# ......(1)

Equation parallel to the current, she paddles upstream

#(v_R-6sin 30)t=200# .....(2)

Using (1) to rewrite (2) we get

#(v_R-6sin 30)xx400/(6 cos30)=200#

#=>v_R=200/400xx(6 cos30)+6sin 30#

#=>v_R=2.6+3#

#=>v_R=5.6\ ms^-1#