Question

A fire hose ejects a stream of water at an angle of 30.1 ° above the horizontal. The water leaves the nozzle with a speed of 25.8 m/s. Assuming that the water behaves like a projectile, how far from a building should the fire hose be located to hit the highest possible fire?

Answer 1

consider the motion along the Y-direction from initial point of launch to point A

v_fy = final velocity at the highest point = 0 m/s

v_oy = initial velocity = v_o Sin $\theta$ = 25.8 Sin30.1 = 12.94 m/s

a = acceleration = - 9.8 m/s²

t = time for the stream to reach the maximum height = ?

using the equation

v_fy = v_oy + at

0 = 12.94 + (- 9.8) t

t = 1.32 sec

consider the motion along the X-direction :

X = horizontal distance travelled by stream before hitting the maximum height = ?

v_ox = initial velocity in X-directon = v_o Cos $\theta$   = 25.8 Cos30.1 = 22.32 m/s

t = time for the stream to reach the maximum height = 1.32 sec

a_x = acceleration along the horizontal direction = 0 m/s²

Using the equation

X = v_ox t + (0.5) a t²

inserting the values

X = (22.32) (1.32) + (0.5) (0) (1.32)²

X = 29.5 m