A fire hose held near the ground shoots water at a speed of 6.5 m/s. At
what angle(s) should the nozzle point in order that the water land 2.5 m
away (Fig)? Why are there two different angles? Sketch the two
trajectories
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We have a projectile motion problem. A fire hose shoots water at 6.5 meters per second. We need to find the angle or angles at which the nozzle should point so that the water lands exactly 2.5 meters away. This is a classic physics problem involving the range formula for projectile motion.
To solve this problem, we use the range formula for projectile motion. The range R equals v-zero squared over g times sine of 2 theta. Substituting our values: 2.5 equals 6.5 squared over 9.8 times sine of 2 theta. This simplifies to 2.5 equals 4.311 times sine of 2 theta. The graph shows how range varies with launch angle, with maximum range occurring at 45 degrees.