Rain drops fall vertically at a speed of 20 m s- 1 . At what angle (in degree) do they fall on the wind screen of a car moving with a velocity 15 m s- 1 , if the wind screen is inclined at an angle of 23° to the vertical? [ . tan -1(0.75) ≈ 37°]

Question

Rain drops fall vertically at a speed of 20 m s- 1 . At what angle (in degree) do they fall on the wind screen of a car moving with a velocity 15 m s- 1 , if the wind screen is inclined at an angle of 23° to the vertical? [ . tan -1(0.75) ≈ 37°] (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-i4nsdisbg6f1.png" /> tan(.90° -θ .)=(20/15) ∴ cotθ =(20/15)=(4/3) ⇒ θ =37° ∴ φ=37° +23° =60° (Angle made with the windscreen)

Q. Rain drops fall vertically at a speed of $20 m s^{- 1}$ . At what angle (in degree) do they fall on the wind screen of a car moving with a velocity $15 m s^{- 1}$ , if the wind screen is inclined at an angle of $2 3^{\circ}$ to the vertical? [ $tan^{- 1} (0.75) \approx 3 7^{\circ}]$

$t an (9 0^{\circ} - θ) = \frac{20}{15}$
$∴ co tθ = \frac{20}{15} = \frac{4}{3}$
$\Rightarrow θ = 3 7^{\circ}$
$∴ ϕ = 3 7^{\circ} + 2 3^{\circ} = 6 0^{\circ}$ (Angle made with the windscreen)

Q. Rain drops fall vertically at a speed of 20ms−1 . At what angle (in degree) do they fall on the wind screen of a car moving with a velocity 15ms−1 , if the wind screen is inclined at an angle of 23∘ to the vertical? [ tan−1(0.75)≈37∘]

tan(90∘−θ)=1520​ ∴cotθ=1520​=34​ ⇒θ=37∘ ∴ϕ=37∘+23∘=60∘ (Angle made with the windscreen)

Q. Rain drops fall vertically at a speed of $20 m s^{- 1}$ . At what angle (in degree) do they fall on the wind screen of a car moving with a velocity $15 m s^{- 1}$ , if the wind screen is inclined at an angle of $2 3^{\circ}$ to the vertical? [ $tan^{- 1} (0.75) \approx 3 7^{\circ}]$

$t an (9 0^{\circ} - θ) = \frac{20}{15}$
$∴ co tθ = \frac{20}{15} = \frac{4}{3}$
$\Rightarrow θ = 3 7^{\circ}$
$∴ ϕ = 3 7^{\circ} + 2 3^{\circ} = 6 0^{\circ}$ (Angle made with the windscreen)