Answer to Question #290947 in Mechanics | Relativity for mhjo

Question

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?

Answer 1

Solution.

$v_r=2.0 km/h;$

$v_s=1.5 km/h;$

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

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

$tan\alpha=\dfrac{2}{1.5}=1.33; \alpha=53^o$

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

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

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

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

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

$b. t=0.1h.$