Exams › JEE Advanced › Physics

Two aircraft start simultaneously from positions A and B respectively (along a straight line toward C) when there is no wind. On a windy day, both head toward C but land at point D instead, reaching D in the same time it would have taken them to reach C. The wind is blowing in the direction:

1. North-West
2. North-East
3. At an angle 0 < theta < 90 deg (but not 45 deg) west of north
4. Due North

Correct answer: At an angle 0 < theta < 90 deg (but not 45 deg) west of north

Solution

Both aircraft maintain heading toward C with the same airspeed. The wind adds a constant velocity vector w to both. They take the same time as they would without wind (time to reach C). This means the wind component along AC must be zero (otherwise travel time changes). So wind is perpendicular to AC. But then both aircraft drift the same distance to one side of C, landing at D. If AC is along north, wind must be east-west (pure west or east). However the original Hindi options say the wind makes an angle 0 < theta < 90 deg west of north (not exactly north-west = 45 deg), which suggests the line AC is not aligned with cardinal directions, making the perpendicular direction oblique.

Related JEE Advanced Physics questions

• Rain is falling at an angle α with respect to the vertical at a velocity of 10 m/s. A girl runs in the opposite direction to the rain at a speed of 8 m/s and observes that the rain appears to make an angle β with the vertical. What is the relationship between α and β?
• A vector A is turned by a very small angle Δθ radians (where Δθ is much less than 1) to form a new vector B. What is the magnitude of the difference |B − A|?
• A swimmer moves through water at a speed of v relative to the water. To cross a river of width d, which flows at a speed u (where u < v), the downstream displacement caused by the river's flow is x. Which of the following is accurate?
• A particle is launched from a point with an initial speed u at an angle θ above the horizontal. At a specific point during its motion, its velocity becomes perpendicular to its original direction. What is the time taken to reach this point?
• A particle of mass m is projected form the ground with an initial speed u₀ at an angle α with the horizontal. At the highest point of its trajectory, it makes a completely inelastic collision with another identical particle, which was thrown vertically upward from the ground with the same initial speed u₀. The angle that the composite system makes with the horizontal immediately after the collision is
• A projectile is launched from level ground with an initial velocity v at an angle θ to the horizontal. The range of the projectile is initially d when the gravitational acceleration is g. If, at the peak of its motion, the projectile enters a zone where the effective gravitational acceleration becomes g' = g/0.81, the new range becomes d'. What is the value of n?

⚔️ Practice JEE Advanced Physics free + battle 1v1 →