A boy and a girl both swim at 3.0 m/s. They jump into ariver 1.0 km across, with

Question

A boy and a girl both swim at 3.0 m/s. They jump into ariver 1.0 km across, with a current of 2.0 m/s [E]. a) The boy faces due north at all times. What is hisvelocity relative to the ground? b) The girl swims straight across relative to the shore. What is her velocity relative to the ground? c) How long (in minutes) does each take to cross theriver? Thanks! A boy and a girl both swim at 3.0 m/s. They jump into ariver 1.0 km across, with a current of 2.0 m/s [E]. a) The boy faces due north at all times. What is hisvelocity relative to the ground? b) The girl swims straight across relative to the shore. What is her velocity relative to the ground? c) How long (in minutes) does each take to cross theriver? Thanks!

Explanation / Answer

Boy: vE = 2 m/s    speed ofcurrent          vN = 3 m/s     swimmingspeed vboy = (4 + 9) = 3.61m/s    direction:   tan = 3 / 2 =1.5   and = 56.3 deg N of E Girl:   VNW = 3m/s   swims in north westerly direction to travelstraight across           22 + vN2 =vNW2 =32        VN = 2.24 m/s    girls speed in northerlydirection                                                        tan = 2.24 / 2   = 48.2 deg N of W Time for boy to cross = 1000 / 3 = 333 sec Time for girl to cross = 1000 / 2.24 = 446 sec

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