Home Physics Motion in a Straight Line Relative Motion A pipe which can rotate in a vertical plane …
Physics Motion in a Straight Line Relative Motion Subjective Type
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.

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The 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 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.

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