Question #290947

A swimmer jumps into a river and swims

straight for the other side at 1.5 km/h [N]

relative to the water. There is a current in the

river of 2.0 km/h [W].

a. What is the swimmer’s velocity relative

to the ground? [2.5 km/h [N53°W]]

b. If the river is 150 m wide, how long will

it take them to cross the river?


1
Expert's answer
2022-01-26T15:30:54-0500

Solution.

vr=2.0km/h;v_r=2.0 km/h;

vs=1.5km/h;v_s=1.5 km/h;

a.v=vr2+vs2;a. v=\sqrt{v_r^2+v_s^2};

v=4+2.25=2.5km/h;v=\sqrt{4+2.25}=2.5km/h;

tanα=21.5=1.33;α=53otan\alpha=\dfrac{2}{1.5}=1.33; \alpha=53^o


b.L=dcosα;b. L=\dfrac{d}{ cos \alpha}; d=150m;d=150m;


L=1500.6018=250m;L=\dfrac{150}{0.6018}=250m;


t=Lv;t=\dfrac{L}{v};


t=2502500=0.1h;t=\dfrac{250}{2500}=0.1h;

Answer:a.v=2.5km/h;α=53o;a. v=2.5km/h; \alpha=53^o;

b.t=0.1h.b. t=0.1h.




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