Question

A boat propelled so as to travel with a speed of 0.50m/s in still water, moves directly (in a straight line ) across a river that is 60m wide. The river flows with a speed of 0.30m/s. how long in seconds does it take the boat to cross the river ?

Answer 1

Answer on Question 47905, Physics, Mechanics | Kinematics | Dynamics

Question:

A boat propelled so as to travel with a speed of $0.50\mathrm{m / s}$ in still water, moves directly (in a straight line) across a river that is $60\mathrm{m}$ wide. The river flows with a speed of $0.30\mathrm{m / s}$ . How long in seconds does it take the boat to cross the river?

Solution:

Let the $\overrightarrow{V_b}$ is the boat speed in still water, $\overrightarrow{V_b}$ is the speed of river and $\overrightarrow{V_{net}}$ is the net speed of the boat, and let us build the vector diagram. In order to find $\overrightarrow{V_{net}}$ we apply the Pythagorean theorem:

$$V _ {n e t} = \sqrt {(V _ {b}) ^ {2} - (V _ {r}) ^ {2}} = \sqrt {\left(0 . 5 \frac {m}{s}\right) ^ {2} - \left(0 . 3 \frac {m}{s}\right) ^ {2}} = 0. 4 \frac {m}{s}$$

Now when we obtain the net speed of the boat, we can find the time that take the boat to cross the river:

$$t = \frac {S}{V _ {n e t}} = \frac {6 0 m}{0 . 4 \frac {m}{s}} = 1 5 0 s$$

Answer:

$$t = 1 5 0 s$$