a fire hose held near the ground shoots water at a speed of 6.4m/s at what angle should the nozzle point in order that the water lands 2.5m away? And why are there two different angles?

Answer 1

the range equation is ... R = [v^2 * sin(2Θ)] / g
... v is the launch velocity
... Θ is the launch angle
... g is gravitational acceleration

plug in the given values and solve for Θ

there are two solutions
... a higher, looping trajectory
... and a lower, flatter trajectory