Projectile Motion?

Question

A fire hose held near the ground shoots water at a speed of 13m/s. At what angle(s) should the nozzle point in order that the water land 16 m away? Why are there two different angles?

Answer 1

The motion of the water molecules will be in a parabola.

x(t)=cos(th)*13*t

and vy(t)=sin(th)*13-g*t

when vy(t)=0, the water reaches apogee, which is 1/2 the flight time

t=sin(th)*13/g

plug 2X this t into x(t)

16=cos(th)*13*2*sin(th)*13/g

16*9.81/13^2=sin(2*th)

th = 34 degrees

th also is 90-34 or 56 degrees

The reason there are two angles is because the water must rise to apogee and descend to strike 16 m away at an angle of greater than and less than 45 degrees. The only solution that has one angle is 45 degrees. Note that sin(45)=cos(45)

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