Published by:
CGP EDU Academic Team
Published on: September 12, 2026
A pipe which can rotate in a vertical plane is mounted on a cart. The cart moves uniformly along a horizontal path with a speed v 1 = 2 m/s. At what angle α to the horizontal should the pipe be placed so that drops of rain falling vertically with a velocity v 2 = 6m/s move parallel to the axis of the pipe without touching its walls ? Consider the velocity of the drops as constant due to the resistance of the air.

Text Solution
Verified by ExpertsThe correct answer is:
A
Given the horizontal velocity of the cart, \( v_1 = 2 \, \text{m/s} \), and the vertical velocity of the rain drops, \( v_2 = 6 \, \text{m/s} \).
To find the angle \( \alpha \) with respect to the horizontal, we use the concept of relative velocities. The pipe will align with the effective velocity of the raindrops relative to the moving cart.
The effective velocity of the raindrops can be represented by a resultant vector from the horizontal and vertical components which can be computed as follows:
The angle \( \alpha \) can be represented using the tangent function:
$$ \tan(\alpha) = \frac{v_{vertical}}{v_{horizontal}} = \frac{6}{2} = 3 $$
Therefore, to find the angle \( \alpha \):
$$ \alpha = \tan^{-1}(3) \approx 71.57^\circ $$
Thus, the angle at which the pipe should be placed is approximately \( 71.57^\circ \). Since the question asks for the angle to the horizontal, we accept this value as the final answer.
To find the angle \( \alpha \) with respect to the horizontal, we use the concept of relative velocities. The pipe will align with the effective velocity of the raindrops relative to the moving cart.
The effective velocity of the raindrops can be represented by a resultant vector from the horizontal and vertical components which can be computed as follows:
- The horizontal component (velocity of the cart): \( v_{horizontal} = v_1 = 2 \, \text{m/s} \)
- The vertical component (velocity of the rain): \( v_{vertical} = v_2 = 6 \, \text{m/s} \)
The angle \( \alpha \) can be represented using the tangent function:
$$ \tan(\alpha) = \frac{v_{vertical}}{v_{horizontal}} = \frac{6}{2} = 3 $$
Therefore, to find the angle \( \alpha \):
$$ \alpha = \tan^{-1}(3) \approx 71.57^\circ $$
Thus, the angle at which the pipe should be placed is approximately \( 71.57^\circ \). Since the question asks for the angle to the horizontal, we accept this value as the final answer.
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems
Two trains, each 50 m long are travelling in opposite direction with velocity 10 m/s and 15 m/s . T…
A 120 m long train is moving in a direction with speed 20 m/s . A train B moving with 30 m / s in t…
A 210 meter long train is moving due North at a of 25m/s. A small bird is flying due South a little…
A police jeep is chasing with, velocity of 45 km / h a thief in another jeep moving with velocity 1…
A boat is sent across a river with a velocity of 8 km/hr. If the resultant velocity of boat is 10 k…
A train of 150 meter length is going towards north direction at a speed of 10 cm/sec . A parrot fli…