A tank moves upward at uniform 1 m s⁻¹. Water leaves its hole horizontally at 2 m s⁻¹ relative to tank. A ground tray spans x = 10 to 12 m from initial hole location. The duration for which water hits the tray is 11t s; determine t (g = 10 m s⁻²). [See Image.]
Physics · Mixed Chapter
JEE Main Practice

Question

A tank moves upward at uniform 1 m s⁻¹. Water leaves its hole horizontally at 2 m s⁻¹ relative to tank. A ground tray spans x = 10 to 12 m from initial hole location. The duration for which water hits the tray is 11t s; determine t (g = 10 m s⁻²). [See Image.]

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1 — For a jet reaching horizontal distance x, flight time after leaving tank is τ = x/2, since horizontal speed is 2 m s⁻¹. Step 2 — If liquid is emitted at tank time tₑ, its starting height is y = tₑ (tank rises at 1 m s⁻¹). Droplet initial vertical speed is +1 m s⁻¹. Step 3 — At ground arrival, 0 = tₑ + τ − (1/2)gτ², so tₑ = 5τ² − τ. Step 4 — Near and far edges x=10 and x=12 correspond to τ = 5 s and 6 s: tₑ,near = 120 s, tₑ,far = 174 s. Step 5 — Duration = 54 s. Since source says 11t s,…