Question

A boat is crossing a wide river flowing at 8 km/hr from east to west. The landing port is exactly opposite the starting point in the north bank of the river. If the boat moves at 10 km/hr towards the other bank and crosses the river, what is the width of the river?

• A. 6 km
• B. 8 km
• C. 10 km
• D. 1.8 km

Hint:

Whenever perpendicular velocities act (like river flow + boat speed), the effective crossing speed is found using the Pythagorean theorem.

Answer 1

The Correct Option is A

Step 1: Understanding the motion.
The boat aims straight north (towards the opposite bank), moving at 10 km/hr. The river flows east-to-west at 8 km/hr. These two velocities are perpendicular, forming a right-angled triangle.

Step 2: Determine the actual width crossed.
Since the boat reaches the point exactly opposite its start, its effective northward velocity is the component responsible for crossing the river: \[ v_{\text{north}} = \sqrt{10^2 - 8^2} \] \[ v_{\text{north}} = \sqrt{100 - 64} = \sqrt{36} = 6 \text{ km/hr} \]
Step 3: Time taken to cross.
The boat uses its full velocity (10 km/hr) to move north, but because 8 km/hr is lost sideways, the *effective* crossing speed is 6 km/hr. Crossing time is 1 hour (because 10 km/hr is the boat's effort but only 6 km/hr moves it north). Thus the width covered is: \[ \text{Width} = v_{\text{north}} \times 1 = 6 \text{ km} \]
Step 4: Conclusion.
Hence, the river is 6 km wide, making (A) the correct answer.