Speed of Raindrops Relative to Ground: 31.93 m/s

[roam]

Homework Statement

A train travels due South at 30 m/s (relative to the ground). It is raining and the rain is being blown towards the South by a strong wind. The path of each raindrop makes an angle of 70° with the vertical, as measured by an observer stationary on the ground. An observer on the train however sees the drops fall perfectly vertically. Determine the speed of the raindrops relative to the ground.

The Attempt at a Solution

The correct answer should be 31.93 m/s, but I have absolutely no clue on how to approach this problem. How can we relate the velocity of the train with the angle of the raindrops? Any guidance is very much appreciated.

 

[pat666]

you've been doing relative velocity??

 

[cartonn30gel]

Homework Statement

A train travels due South at 30 m/s (relative to the ground). It is raining and the rain is being blown towards the South by a strong wind. The path of each raindrop makes an angle of 70° with the vertical, as measured by an observer stationary on the ground. An observer on the train however sees the drops fall perfectly vertically. Determine the speed of the raindrops relative to the ground.

That sentence in bold is the key to understand the problem. If the rain drops are falling vertically with respect to an observer on the train, then what can you say about the horizontal components of their velocities?

 

[roam]

That sentence in bold is the key to understand the problem. If the rain drops are falling vertically with respect to an observer on the train, then what can you say about the horizontal components of their velocities?

The horizontal component of the velocity of train relative to ground is 30 m/s. So the horizontal components of the velocity of the rain relative to train is 30 cos 90 = 0??

 

[Daft]

Don't think too much about calculations relative to the train, you've got the right idea

Maybe this diagram will help: http://img571.imageshack.us/f/trainr.jpg/

(When I put it in [ img ] tags it didn't show up)

 

[roam]

Thank you very much, Daft. It worked out!