Answer to Question #110269 in Mechanics | Relativity for samia tasmim

Question

The velocity of water flow in a river is 10ms-1. The width of the river is 100 meters. Two boatman are having a race for reaching the other side of the river. Boatman 1 can drive his boat with velocity 15ms-1 in still water; and Boatman 2 can drive his boat with a constant acceleration of 4.5 ms-2 in still water. Who wins the race? (Note: Both of the boatmen are good at physics and thus follow the path which will be most efficient. Also note that, the one who reaches the opposite side of the river first wins, regardless of their position the reach at. i.e. they don’t need to end up exactly at the opposite side of where they started)

Answer 1

$$d=vt_1\to 100=15t_1$$

$$t_1=6.67\ s$$

$$d=0.5at_2^2\to 100=0.5(4.5)t_2^2$$

$$t_2=6.67\ s$$

We can see that both of the boatmen will reach the other side of the river at the same time.