A 200 g projectile is launched in a viscous medium at 60° with initial speed 270 m s⁻¹. It experiences linear drag F = -cv, where c = 0.1 kg s⁻¹. It hits a vertical wall after 2 s. Taking e = 2.7, find the horizontal distance of the wall from the point of projection in metres.
Physics · Kinematics part-2 Projectile Motion · Ground to ground projectile
JEE Advanced 2025 Paper 2

Question

A 200 g projectile is launched in a viscous medium at 60° with initial speed 270 m s⁻¹. It experiences linear drag F = -cv, where c = 0.1 kg s⁻¹. It hits a vertical wall after 2 s. Taking e = 2.7, find the horizontal distance of the wall from the point of projection in metres.

Physics · Kinematics part-2 Projectile Motion · Ground to ground projectile

G1 Physics · Accepted Answer

Horizontal motion obeys

m dvₓ/dt = −cvₓ.

Thus vₓ = vₓ₀e⁻ᶜᵗᐟᵐ.

Here m = 0.2 kg, c/m = 0.5 s⁻¹, vₓ₀ = 270cos60° = 135 m s⁻¹.

Hence x(2) = ∫₀² 135e⁻⁰⋅⁵ᵗ dt = 270(1−e⁻¹).

Using e=2.7: x = 270(1−1/2.7) = 170 m.