Balloon rising 4m/s, wind blow horizontal at speed of 4.5m/s find the velocity of balloon relative to the ground?
Looks like good ol' Pythagoras to me
use vector addition on the two components ... a^2 + b^2 = c^2
To find the velocity of the balloon relative to the ground, we need to combine the vertical velocity (balloon rising) and the horizontal velocity (wind blowing). This can be done using vector addition.
Since the balloon is rising at a velocity of 4 m/s, we can consider this as the vertical velocity component. And since the wind is blowing horizontally at a velocity of 4.5 m/s, we can consider this as the horizontal velocity component.
To find the resulting velocity, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).
In this case, the vertical velocity (4 m/s) is the magnitude of side a, and the horizontal velocity (4.5 m/s) is the magnitude of side b. The resulting velocity (relative to the ground) will be the magnitude of the hypotenuse (c).
Using the Pythagorean theorem, we can calculate the resulting velocity:
c^2 = a^2 + b^2
c^2 = (4 m/s)^2 + (4.5 m/s)^2
Simplifying this equation, we get:
c^2 = 16 m^2/s^2 + 20.25 m^2/s^2
c^2 = 36.25 m^2/s^2
Taking the square root of both sides, we find:
c ≈ 6.02 m/s
Therefore, the velocity of the balloon relative to the ground is approximately 6.02 m/s.