How do you calculate the speed in this problem ?

Question

Calculate the speed of raindrops hitting your face when they fall vertically at 3m/s while you're running horizontally at 4m/s.

Answer 1

This is really just adding two vectors together: one is the speed of raindrop and the other your running speed.

You can draw it out on on grid with your running speed on the x-axis and the raindrop speed on the y-axis.  The vector created by adding the two together is speed the raindrops hit your face.

y(m/s)

_

3-------------------*

|                    

2                  

|                    

1                  

|                    

----1----2----3----4----5---  x (m/s)

Speed of raindrop hitting face, s, is the length of the line from the origin to the * (not sure how to draw that using text).

s = sqr_root (x^2 + y^2) = sqr_root (4(m/s)^2 + 3(m/s)^2) = 5 (m/s)

Answer 2

Use Pythagoreans therm

3^2+4^2=s^2

9+16=s^2

25=s^2

s=sqrt(25)

s=5m/s

When ever you have a horizontal and vertical (x and y components) forces and you want to find the resultant force just use Pythagoreans theorem.

Answer 3

I'm not sure, bit logically speaking, I think they would still be hitting your face at 3 m/s because the speed you are running doesn't affect how fast the rain drops are falling from the sky.