Finding the Speed of Rain in Relative Motion

[kalupahana]

Relative motion prob, please help

Homework Statement

A man walk at a rate of 2 km/h; A rain appears to fall vertically. when he doubled his speed it appears to fall at 30^o vertical. Find the real speed of the rain.

Homework Equations

The Attempt at a Solution

Help me to do this question. I cannot understand what my teacher said about relative motion. Please explain me how find the answer for this question.

 

[tiny-tim]

hi kalupahana!

let V_MG be the velocity of the Man relative to the Ground,
V_RG be the velocity of the Rain relative to the Ground,
and V_RM be the velocity of the Rain relative to the Man

then draw a vector triangle MRG for each of the two situations: the length of the RG side will be the same in both triangles, and the length of the MG side will be 2 in one triangle and 4 in the other triangle

(see the pf library entry on vector triangle for some more details)

 

[kalupahana]

hi kalupahana!

let V_MG be the velocity of the Man relative to the Ground,
V_RG be the velocity of the Rain relative to the Ground,
and V_RM be the velocity of the Rain relative to the Man

then draw a vector triangle MRG for each of the two situations: the length of the RG side will be the same in both triangles, and the length of the MG side will be 2 in one triangle and 4 in the other triangle

(see the pf library entry on vector triangle for some more details)

In both instance V_RM is constant.
then sin60 = 2/x

x = 4/√3 = 2.3 km/h

is this right

 

[tiny-tim]

In both instance V_RM is constant.

No, V_RG is constant (it's the same Rain, so its velocity relative to the Ground is the same).

Try again … draw the two triangles, with a shared side …

what does it look like? ​

 

[kalupahana]

No, V_RG is constant (it's the same Rain, so its velocity relative to the Ground is the same).

Try again … draw the two triangles, with a shared side …

what does it look like? ​

I got triangle like this

then tan60 = V^RG /4
4√3 = V_RG

 

[tiny-tim]

hi kalupahana!

(just got up :zzz: …)

That's the right idea, but you've misinterpreted the question.

Your diagram show the rain falling vertically, but it doesn't.

Also, your arrows are going the wrong way round each vector triangle …

they have to match up so that V_RG = V_RM + V_MG

(or V_RM = V_RG + V_GM = V_RG - V_MG).

Try again. ​