A cannon shoots a shell straight up. It reaches its maximum height, 1,051 feet, and splits into two pieces, one weighing 2 lb and the other 4 lb. The two pieces are observed to strike the ground simultaneously. The 4 lb piece hist the ground 1,608 feet away from the explosion (measured along the x axis). How long would it have taken the shell to return to the ground if it has not split? (answer to two decimal points)

To find the time it would have taken the shell to return to the ground if it had not split, we will use the fact that the two pieces hit the ground simultaneously. We can start by finding the time it takes for the 4 lb piece to hit the ground.

Let's assume the initial velocity of the shell is denoted as "v".

Using the kinematic equation for vertical motion, the maximum height reached by the shell can be calculated as:

h = (v^2) / (2g)

Here, g represents the acceleration due to gravity (32 ft/s^2).

Plugging in the given maximum height (1,051 ft), we can solve for the initial velocity:

1,051 = (v^2) / (2 * 32)

Simplifying the equation, we get:

v^2 = 1,051 * 2 * 32
v^2 = 67,232

Taking the square root of both sides, we find:

v ≈ 259.35 ft/s

Now, we can determine the time it takes for the 4 lb piece to hit the ground by considering its horizontal distance traveled (1,608 ft) and the initial velocity (v ≈ 259.35 ft/s).

Using the formula for horizontal motion, we can calculate the time:

d = vt

Rearranging the formula, we get:

t = d / v

Substituting the given values, we have:

t = 1,608 ft / 259.35 ft/s

Calculating this gives us:

t ≈ 6.20 s

Therefore, it would have taken the shell approximately 6.20 seconds to return to the ground if it had not split.

There IS no question

sorry I don't know what happened but I posted it again and the question is on there.