Afirefighter wishes to aim his fire hose such that the stream of water goes directly into the second story which has caught on fire. the second story window is at a height of 20 m above the ground. water exits the fire hose at a speed 25 m/s and the firefighter aims it at an angle 60°. how far from the building must he stand?

Since the water stream forms an arc, this can be solved using the derived equation for projectile motions. In particular, we use the equation for the trajectory of a projectile:

y = xtanθ + gx/2v²cosθ
where
y = 20 m
θ = 60°
g = 9.81 m/s²
v = 25 m/s

Substituting the values:
20 = xtan60° + (9.81)x/2(25)²cos60°
Solving for x,
x = 11.44 m

Therefore, the firefighter must be 11.44 m away from the base of the building.

Figure it out your self