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

from 1609, galileo galilei used the recently invented telescope to observe the sun, moon and planets. he saw the mountains and craters of the moon, and for the first time revealed the planets to be worlds in their own right. galileo also provided strong observational evidence that planets orbited the sun.

his discoveries about the moon, jupiter's moons, venus, and sunspots supported the idea that the sun - not the earth - was the center of the universe, as was commonly believed at the time.galileo turned his gaze toward venus, the brightest celestial object in the sky - other than the sun and the moon.