What Are the Two Angles for a Fire Hose to Reach 2.0 Meters?

[MIA6]

Homework Statement

A fire hose held near the ground shoots water at a speed of 6.8 m/s. At what angle(s) should the nozzle point in order that the water land 2.0 m away? Why are there two different angles?

The Attempt at a Solution

First, I don't know why there would be two angles. I only found the formula, but I don't know how to solve the angle out. I found t=2* 6.8sinangle/9.81(I don't know how to use the angle symbol) dx=vix*t, 2=6.8cosangle*2*6.8sinangle/9.81. How to find the angle?

Thank you.

 

[MIA6]

I found t=2* 6.8sin(angle)/ 9.81. dx=vix*t, 2=6.8cos(angle)*2*6.8sin(angle)/9.81. How to find the angle? I rewrite it because I just want to make sure you understand what I am talking about. Really hope someone can help me! thanks.

 

[m2003]

I can provide some insights into the physics behind the fire hose projectile. The angle at which the nozzle should point in order for the water to land 2.0 m away depends on the initial velocity and the acceleration due to gravity. This is because the water from the fire hose follows a parabolic trajectory, with the initial velocity and gravity determining the shape and range of the curve.

To solve for the angle, we can use the formula for projectile motion: x = v0 * cos(theta) * t and y = v0 * sin(theta) * t - (1/2) * g * t^2, where x and y are the horizontal and vertical distances, v0 is the initial velocity, theta is the angle, t is the time, and g is the acceleration due to gravity.

In this case, we know that x = 2.0 m, v0 = 6.8 m/s, and g = 9.81 m/s^2. We can also calculate t by using the formula x = v0 * t, where x is the distance and v0 is the initial velocity. Substituting these values into the equation for y, we get: 2.0 = 6.8 * sin(theta) * t - (1/2) * 9.81 * t^2.

To solve for theta, we can rearrange the equation to get: 0 = 4.9 * t^2 - 6.8 * sin(theta) * t + 2.0. This is a quadratic equation, and we can solve for t using the quadratic formula. Once we have t, we can plug it back into the equation for x and solve for theta.

Now, you may have noticed that there are two angles that could satisfy this equation. This is because there are two possible trajectories that the water could follow to land 2.0 m away. One angle would result in the water being launched at a higher angle and reaching the target in a shorter amount of time, while the other angle would result in the water being launched at a lower angle and taking a longer time to reach the target. Both angles will result in the water landing 2.0 m away, but they will have different flight paths.

In conclusion, there are two different angles that could result in the water landing 2.0 m away because of the parabolic trajectory of the water