Posted by **BOB** on Thursday, November 10, 2011 at 8:42pm.

a hot air balloon is rising vertically 10 ft/sec while the wind is blowing horizontally 5ft/sec. Find the speed of the balloon and the angle x that it makes with the horizontal.

I know that the speed of the balloon is

the square root of (10)^2 + (5)^2, but I was wondering if someone could tell me why the speed is equal to that. Thanks.

- Math, Please Help!!! -
**Reiny**, Thursday, November 10, 2011 at 9:45pm
from the origin draw a vertical line of length 10

from the origin draw a horizontal line of length 5

Complete the rectangle, and draw in the diagonal.

That diagonal is the resultant velocity.

You now have a right-angled triangle with base of 5 and height of 10

let the hypotenuse be h

h^2 = 10^2+5^2 = 125

h = √125 = 5√5 = appr. 11.18

to find the angle

sinx = 10/11.18

x = 63.4°

we could have done : tanx = 10/5 = 2

x = 63.4°

- Math, Please Help!!! -
**Steve**, Friday, November 11, 2011 at 10:30am
You can draw a triangle for velocity, even though usually you do it for distances, because the distance is velocity * time. The time elapsed is just a scale factor, so the velocity triangle is just the distance triangle, scaled by how much time has elapsed.

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