ACTIVITY 3: How high and how farA fire fighter aims a fire hose upward, toward a fire in a skyscraper. The water leaving thehose has a velocity of 32.0 m/s. If the fire fighter holds the hose at an angle of 78.5°, whatis the maximum height and range of the water stream? (Write your answer in yournotebook)Note: The water droplets leaving the hose can be treated as projectiles
Question
ACTIVITY 3: How high and how farA fire fighter aims a fire hose upward, toward a fire in a skyscraper. The water leaving thehose has a velocity of 32.0 m/s. If the fire fighter holds the hose at an angle of 78.5°, whatis the maximum height and range of the water stream? (Write your answer in yournotebook)Note: The water droplets leaving the hose can be treated as projectiles
Solution
To solve this problem, we need to use the equations of motion for a projectile.
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First, we need to find the components of the initial velocity in the x and y directions.
The initial velocity in the x direction (Vx) is given by V*cos(θ) = 32.0 m/s * cos(78.5°) = 7.03 m/s.
The initial velocity in the y direction (Vy) is given by V*sin(θ) = 32.0 m/s * sin(78.5°) = 31.4 m/s.
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Next, we find the time it takes for the water to reach its maximum height. This is when its velocity in the y direction is zero.
We use the equation Vy = u - gt, where u is the initial velocity in the y direction, g is the acceleration due to gravity (9.8 m/s²), and t is time.
Solving for t gives us t = u/g = 31.4 m/s / 9.8 m/s² = 3.2 s.
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We can now find the maximum height using the equation h = ut - 0.5gt², where h is the height, u is the initial velocity in the y direction, g is the acceleration due to gravity, and t is time.
Substituting the values we have gives us h = 31.4 m/s * 3.2 s - 0.5 * 9.8 m/s² * (3.2 s)² = 50.4 m.
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Finally, we find the range (the horizontal distance the water travels) using the equation d = Vx*t, where d is the distance, Vx is the initial velocity in the x direction, and t is time.
Substituting the values we have gives us d = 7.03 m/s * 3.2 s = 22.5 m.
So, the maximum height of the water stream is 50.4 m and the range is 22.5 m.
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