A tank of height H is filled with water and sits on the ground, as shown in the figure. Water squirts from a hole at a height y above the ground and has a range R. For two y values, 0 and H, R is zero. Determine the value of y for which the range will be a maximum. (Use any variable or symbol stated above as necessary.)

Question

y =

Answer 1

first, find the velocity of the water comingout of the hole with bernoulls equation.

Then, range= velocity*timetofall

but time to fall t is found by

y=gt or t= y/g

range= velocity(y)*t/y

then take the derivative of range with respect to y.

Answer 2

first, find the velocity of the water comingout of the hole with bernoulls equation.

Then, range= velocity*timetofall

but time to fall t is found by

y=gt or t= y/g

range= velocity(y)*g/y

then take the derivative of range with respect to y.