Question

Two swimmers Chris and Sarah starts together at the same point on the bank of a wide stream that lows with a speed v. Both move at the same speed c (where c>v) relative to the water. Chris swims downstream a distance L and thenupstream the same distance. Sarah swims so that her motion relative to the Earth is perpendicular to the banks of the stream. She swims the distance L and then back the same distance , with both swimmers returning to the starting point. a) In terms of L, c, and v find the timer interval required for Chris round trip delta t_= b) In terms L c and v find the time i

Answer 1

interval required for sarahs round trip. delta t_2=.....c) explain which swimmer returns first

Answer 2

Chris:
swims downstream at rate (c+v)
swims upstream at rate (c-v)
t = L/(c+v) + L/(c-v) = [L(c-v) +L(c+v)]/(c^2 -v^2) = 2Lc/(c^2 -v^2)

Sarah:
swims at right angle relative to bank
x = sqrt(c^2 -v^2)
t = 2L/x = 2L/ sqrt(c^2 -v^2) = (2L)^2/(c^2 -v^2)

if c < 2L, then Chris finishes first
c = 2L, they finish at same time
c > 2L, then Sarah finishes first

Answer 3

oops i messed up at the end.
For Sarah, i squared t for some reason
t = 2L/sqrt(c^2 -v^2)

Answer 4

Sarah finishes first

2L/sqrt(c^2-v^2) < 2Lc/(c^2-v^2)

Answer 5

Thank you so much this is really helping. I understood everything except the part where x=root c^2-v^2 for sarah...how so?

Answer 6

its just like the airplane problem, the 2 vectors with the resultant vector make a right triangle (see drawing)
the magnitude of resultant vector (speed) is root c^2 -v^2

Answer 7

Oh right right pythagorean theorem. I missed that part ok. Thanks!