A firefighter 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?

Question

Mathematics

Julien

10 September, 19:17

A firefighter 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?

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Mekhi Friedman · Answer 1

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.