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Question #42078

Difficulty: 8/10 | 🟢 Free

The Question

A train carriage is accelerating horizontally on a straight track with a constant acceleration $a = \frac{g}{\sqrt{3}}$ , where $g$ is the acceleration due to gravity. A passenger inside the carriage projects a ball from the horizontal floor with an initial speed $u$ relative to the carriage, at an angle $\alpha$ with the floor, in the direction of the carriage's acceleration. If the ball has the same horizontal range on the floor for two distinct angles of projection $\alpha_1$ and $\alpha_2$ , find the sum $\alpha_1 + \alpha_2$ .

Options

A.
$\frac{\pi}{2}$
B.
$\frac{\pi}{3}$
C.
$\frac{\pi}{4}$
D.
$\frac{2\pi}{3}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Intuition_Breaker

Train your brain to resist "obvious" answers that are designed to deceive your intuition.

Concepts Behind This Question

Horizontal Range Invariance|Relative Velocity in 2D|Apparent Weight in Accelerating Elevators|Vector Cross-Products

Why This Question Is Tricky

Common Mistakes

This question tests the invariance of horizontal range in a non-inertial reference frame.

A common trap is assuming that complementary angles (summing to $\pi/2$ ) always yield the same range.

However, when the launch frame accelerates horizontally, the pseudo-force introduces a horizontal acceleration component to the projectile's relative motion.

This tilts the effective gravity vector, breaking the standard symmetry.

Students must derive the range equation in the non-inertial frame and use trigonometric identities to find the new invariant angle sum, which depends on the ratio of the frame's acceleration to gravity.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Motion in a Plane - Class 11 Part 1
Concept	Horizontal Range Invariance
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free