Projectile Motion: How Far Away Should Water Protectors Stand to Avoid Being Sprayed?

What is the exit velocity of water from a commercially available water cannon that can be mounted on a truck? How far away would the water protectors at Standing Rock have to stand in order not to get sprayed with this water cannon? The exit velocity of water from a commercially available water cannon that can be mounted on a truck is about 100.7 m/s. To avoid the water spray from a cannon that has an exit velocity of 100.7 m/s (assuming air resistance is negligible), the water protectors at Standing Rock would need to stand at least approximately 515.43 m away.

When dealing with a water cannon mounted on a truck with an exit velocity of 100.7 m/s, it is crucial to consider the projectile motion involved. In this scenario, we can neglect air resistance and treat the water cannon as a projectile motion problem. The key parameter to determine the safe distance for water protectors is the horizontal range.

The formula for the horizontal range in projectile motion is:

R = ((v^2) * sin(2*angle))/g

Where: - R is the range - v is the initial velocity (exit velocity of water) - g is the acceleration due to gravity - angle is the angle of projection

Since the angle of the water cannon's projection is not provided, it is common practice to assume a launch angle of 45 degrees. This angle maximizes the range of the projectile. By plugging in the values, we find that the water protectors should stand at least 515.43 meters away to avoid getting sprayed with the water from the cannon.

It's important to note that this calculation provides a general estimation and does not account for factors such as elevation, temperature, or uneven ground. These variables can have an impact on the actual range of the water spray. For a more accurate assessment, additional details would be needed.

Understanding projectile motion can be beneficial in various real-life situations where objects are launched into the air. By applying the principles of physics, we can analyze and predict the path of projectiles, ensuring safety and efficiency in their trajectory.

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