Can you please help me with this Physics problem?

Question

A water hose is used to fill a large cylindrical storage tank of diameter D and height W. The hose shoots the water at 45˚ above the horizontal from the same level as the base of the tank and as is a distance 6D away.For what range of launch speeds will the water enter the tank? Ignore air resistance, and express the answer in terms of D and g.

thanks.

Answer 1

the answer depends on what W is, if W is too high then the water will hit the side of the tank no matter how fast you shoot it

assuming that W is sufficiently small, then

the horizontal range of a projectile is given by

R = v²sin2θ /g

you're given θ = 45 and sin90=1 so this simplifies to

R = v²/g

you need the water to travel a distance

greater than 6D but less than 7D

6D < v²/g < 7D

so v has to be in the range

√(6gD) < v < √(7gD)

.,.,