A tank of height H is filled with water and sits on the ground. 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.)

To find the value of y for which the range will be a maximum, we need to consider the key factors that affect the range.

Let's break down the problem:

1. The height of the tank is given as H.
2. The water squirts from a hole at a height y above the ground.
3. The range, denoted by R, represents the horizontal distance traveled by the water jets before hitting the ground.

Now, let's analyze the factors that affect the range:

1. The horizontal distance traveled by the water jet primarily depends on the initial vertical velocity of the water. The greater the vertical velocity, the larger the range.
2. The vertical velocity of the water jet depends on the kinetic energy of the water as it exits the hole. The kinetic energy depends on the height from which the water exits. Higher exit height results in a higher vertical velocity and, consequently, a larger range.

Based on this analysis, we can determine that the range will be a maximum when the water exits from the highest point possible, which corresponds to y = H.

Therefore, the value of y for which the range is maximum is y = H.