Question

Firefighters use a high-pressure hose to shoot a stream of water at a burning building. The water has a speed of 25.0 m/s as it leaves the end of the hose and then exhibits projectile motion. The firefighters adjust the angle of elevation or of the hose until the water takes 3.00 s to reach a building 45.0 m away. Ignore air resistance; assume that the end of the hose is at ground level.

A. Find the angle of elevation a above the horizontal. Express your answer in degrees.

Answer 1

To find the angle of elevation for the water to reach a building 45.0 meters away in 3 seconds, we calculate the horizontal velocity and then use trigonometry to determine the angle, which is approximately 53.13 degrees.

Step-by-step explanation:

To solve this problem, we will use the principles of projectile motion. We know the water stream reaches the building in 3.00 seconds and the horizontal distance to the building is 45.0 meters.

Since there is no air resistance, the horizontal velocity (vx) remains constant throughout the motion, so we can calculate it using the formula:

vx = distance/time
vx = 45.0 m / 3.00 s = 15.0 m/s

The water leaves the hose with a speed of 25.0 m/s, which is the hypotenuse of the velocity triangle. To find the angle α in degrees, we use trigonometry:

cos(α) = vx / speed of water

cos(α) = 15.0 m/s / 25.0 m/s

α = cos⁻¹(15.0/25.0)

α ≈ 53.13°

The angle of elevation needed is approximately 53.13 degrees above the horizontal.