The question in the image is written in Bengali, and it is related to motion and speed problems in physics. Here is the translation and summary:

Problem: A boat is crossing a river. The boat's speed in still water is given as $8 \, \text{ms}^{-1}$ and the current (river flow) is $12 \, \text{ms}^{-1}$. The river's width is $400 \, \text{m}$.

1. What should be the angle the boat needs to maintain to go straight across the river?
2. How long will it take to cross the river directly?

This is a classic problem of vector resolution where the boat's velocity relative to the river current is the key to solving the problem.

Solution:

1. Finding the angle ($\theta$) the boat must make with the riverbank:

The boat's velocity components can be resolved:

• The velocity of the boat in still water is $8 \, \text{ms}^{-1}$, and it must counteract the river's flow $12 \, \text{ms}^{-1}$.

Using trigonometry: $\sin(\theta) = \frac{\text{River flow velocity}}{\text{Boat's velocity in still water}} = \frac{12}{8} = 1.5$

However, since $\sin(\theta) > 1$, it is impossible for the boat to go directly across in a straight line. The boat will drift downstream, and the boat will take an angular path.

2. Time to cross the river:

To calculate the time taken to cross the river, we use only the boat's velocity perpendicular to the riverbank (assuming the boat's forward motion is along the $x$-axis):

The component of the boat’s velocity along the river width: $v_{\text{perpendicular}} = 8 \, \text{ms}^{-1}$

The time $t$ taken to cross the river: $t = \frac{\text{River width}}{\text{Boat's velocity perpendicular to the flow}} = \frac{400}{8} = 50 \, \text{seconds}$

So, the boat will take 50 seconds to cross the river.

Would you like further details or have any questions? Here are five related questions you might find interesting:

1. How would the problem change if the boat's speed was lower than the river's speed?
2. What if the river width was doubled—how would the time change?
3. How do you calculate the downstream drift in this scenario?
4. What is the importance of relative velocity in such problems?
5. How would the problem be different if there was a bridge across the river?

Tip: Always check if the problem can be simplified using vector components for motion in two dimensions.