A stationary man observes that the rain strikes him at an angle of 60�

1.	A stationary man observes that the rain strikes him at an angle of 60° to the horizontal . When he begins to move with a velocity of 25m/s then the drops appear to strike him at angle 30° from horizontal. Calculate the velocity of rain drop.
Answer» Answer: The VELOCITY of the rain drop is 25 m/s. Explanation: GIVEN data: The angle at which the rain STRIKES the man is 60° from the horizontal. When the velocity of the man, Vm = 25 m/s then, the angle at which the rain strikes the man is 30° from the horizontal. To find: The velocity of rain drop Let’s consider the velocity of rain drop be “Vr”. Now, Component of Vr along the horizontal direction = Vr cos 60° = Vr/2 [SINCE cos 60°=1/2] Component of Vr along the vertical direction = Vr sin 60° = (√3 Vr)/2 [since cos 60°=√3/2] When Vm = 25 m/s then the, Component of Vr along the horizontal direction = [(Vr / 2) + 25] and the vertical component REMAINS the same. Therefore, we can write tan 30° = (Vr along vertical direction) / (Vr along horizontal direction) or, 1 / √3 = [(√3 Vr)/2] / [(Vr / 2) + 25] or, 1 / √3 = [(√3 Vr)] / [(Vr + 50] or, 3Vr = Vr + 50 or, 2Vr = 50 or, Vr = 25 m/s Hence, the velocity of the rain drop Vr = 25 m/s.

A stationary man observes that the rain strikes him at an angle of 60° to the horizontal . When he begins to move with a velocity of 25m/s then the drops appear to strike him at angle 30° from horizontal. Calculate the velocity of rain drop.

Answer»

Answer:

The VELOCITY of the rain drop is 25 m/s.

Explanation:

GIVEN data:

The angle at which the rain STRIKES the man is 60° from the horizontal.

When the velocity of the man, Vm = 25 m/s then, the angle at which the rain strikes the man is 30° from the horizontal.

To find: The velocity of rain drop

Let’s consider the velocity of rain drop be “Vr”.

Now,

Component of Vr along the horizontal direction = Vr cos 60° = Vr/2 [SINCE cos 60°=1/2]

Component of Vr along the vertical direction = Vr sin 60° = (√3 Vr)/2 [since cos 60°=√3/2]

When Vm = 25 m/s then the,

Component of Vr along the horizontal direction = [(Vr / 2) + 25] and the vertical component REMAINS the same.

Therefore, we can write

tan 30° = (Vr along vertical direction) / (Vr along horizontal direction)

or, 1 / √3 = [(√3 Vr)/2] / [(Vr / 2) + 25]

or, 1 / √3 = [(√3 Vr)] / [(Vr + 50]

or, 3Vr = Vr + 50

or, 2Vr = 50

or, Vr = 25 m/s

Hence, the velocity of the rain drop Vr = 25 m/s.