TRACY SWIMS ACROSS A STREAM OF WIDTH 40.0M IN 33.0S WHEN THERE IS NO CURRENT.SHE TAKES 59.0 TO COVER THE SAME DISTANCE WHEN THERE IS CURRENT.FIND THE SPEED OF THE CURRENT RIVER.

Question

TRACY SWIMS  ACROSS A STREAM OF WIDTH 40.0M IN 33.0S WHEN THERE IS NO CURRENT.SHE TAKES 59.0 TO COVER THE SAME DISTANCE WHEN THERE IS CURRENT.FIND THE SPEED OF THE CURRENT RIVER.

bobpursley · Answer

Well, the swimmers velocity in still water is 40/33 m/s=1.21m/s

Now, she is swimming some angle upstream, so the horizontal component of this velocity is 40/57 m/s

Now how far did she swim relative to the water ?

relative to water= 40/33 * 57 meters

CosTheta= 40/(40/33 * 57)= 33/57
Theta= arccos (33/57)=54.6 deg
But Tantheta= current/(40/33 cosTheta)
currentvelocity= tan54.6 *40/57=.99m/s

check my thinking.

ERIC · Answer

thanks men appreciate your help.