Awater hose is used to fill a large cylindrical storage tank of

distance diameter d and height 2d. the hose shoots the water at 45°

above the horizontal from the same level as the base of the tank and is a

distance 6d away. for what range of launch speeds will the water enter

the tank? ignore air resistance, and express your answer in terms of d

and g.

maximum possible speed by solving above equation for 7D is

minimum possible value of speed for solving x = 6D is given as

Explanation:

Let the nozzle of the hose be at the origin. Then the nearest part of the rim of the tank is at (, ) =  (6, 2) and the furthest part of the rim is at (, ) = (7, 2).

The trajectory of the water can be found as follows:

Now from above two equations we have

now we know that height of the cylinder is 2D so we have

by solving above equation we have

now we know that maximum value of x is 7D

so the maximum possible speed by solving above equation for 7D is

minimum possible value of speed for solving x = 6D is given as

the answer is a)

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