Final answer:
A firehouse held near the ground shoots water at the speed of 7.5m/sec, the angle should the nozzle point in order for the water to land 2.0m away is approximately 15 degrees.
Step-by-step explanation:
In order to calculate the angle at which the nozzle should point, we can use the concept of projectile motion.
When water is shot out of a firehouse, it forms a parabolic trajectory.
The horizontal velocity remains constant, while the vertical velocity changes due to the force of gravity.
Using the given information, we can set up the following equation to find the angle:
tan(θ) = Vertical Velocity / Horizontal Velocity
Since the water lands 2.0m away horizontally, we can substitute the known values:
tan(θ) = 2.0m / 7.5m/s
Solving for θ gives us:
θ = arctan(2.0m / 7.5m/s)
Using a calculator, we find that θ ≈ 15 degrees.
Therefore the angle is approximately 15 degrees.