Rain drops fall vertically at a speed of 20 ms -1. At what angle do they fall on the wind screen of a car moving with a velocity of 15 ms -1, if the wind screen velocity inclined at an angle of 23° to the vertical? [ cot -1((4/3)) ≈ 36°]

Question

Rain drops fall vertically at a speed of 20 ms -1. At what angle do they fall on the wind screen of a car moving with a velocity of 15 ms -1, if the wind screen velocity inclined at an angle of 23° to the vertical? [ cot -1((4/3)) ≈ 36°] (A) 60° (B) 30° (C) 45° (D) 90°

Tardigrade Admin · Accepted Answer

Let the required angle is θ. tan (90°-θ)=(20/15) ∴ cos θ=(20/15)=(4/3) ⇒ θ=37° ∴ θ=37°+23°=60°

Q. Rain drops fall vertically at a speed of $20 m s^{- 1}$ . At what angle do they fall on the wind screen of a car moving with a velocity of $15 m s^{- 1}$ , if the wind screen velocity inclined at an angle of $2 3^{\circ}$ to the vertical?
$[cot^{- 1} (\frac{4}{3}) \approx 3 6^{\circ}]$

$6 0^{\circ}$

$3 0^{\circ}$

$4 5^{\circ}$

$9 0^{\circ}$

Let the required angle is $θ$ .
$tan (9 0^{\circ} - θ) = \frac{20}{15}$
$∴ cos θ = \frac{20}{15} = \frac{4}{3}$
$\Rightarrow θ = 3 7^{\circ}$
$∴ θ = 3 7^{\circ} + 2 3^{\circ} = 6 0^{\circ}$

Q. Rain drops fall vertically at a speed of 20ms−1. At what angle do they fall on the wind screen of a car moving with a velocity of 15ms−1, if the wind screen velocity inclined at an angle of 23∘ to the vertical? [cot−1(34​)≈36∘]

60∘

30∘

45∘

90∘