A fire hose a stream of water at an angle of 35degree above the horizontal. The water leaves the nozzle with a speed 25m/s. Assuming that the water behave like a projectile ,how far from a building should the fire hose be located to hit the highest possible fire?
t = v sin35/g
x = v cos35 t
To determine the distance at which the fire hose should be located to hit the highest possible fire, we can solve this problem by analyzing the projectile motion of the water stream. Here's how to approach it:
1. Identify the known values:
- Initial velocity of the water stream, v = 25 m/s
- Launch angle above the horizontal, θ = 35 degrees
- Acceleration due to gravity, g = 9.8 m/s^2
2. Split the initial velocity into its horizontal and vertical components:
- The horizontal component, v_x, remains constant throughout the motion as there is no horizontal acceleration.
- The vertical component, v_y, can be determined using the launch angle and initial velocity:
v_y = v * sin(θ)
3. Calculate the time it takes for the water stream to reach the highest point:
- At the highest point, the vertical velocity becomes zero, so we can use the following formula to find the time taken to reach this point:
0 = v_y - g * t_max
- Rearranging the equation, we have:
t_max = v_y / g
4. Determine the vertical distance covered by the water stream at the highest point:
- Using the formula for vertical position in projectile motion, we have:
Δy = v_y * t_max - (1/2) * g * (t_max)^2
5. Find the horizontal distance covered by the water stream:
- The horizontal distance, d, can be calculated using the horizontal component of velocity and the time taken to reach the highest point:
d = v_x * t_max
6. Calculate the final answer:
- The desired distance from the building should be equal to the horizontal distance covered by the water stream, d.
By following these steps and plugging in the given values, you can find the distance at which the fire hose should be located to hit the highest possible fire.