There air multiple ways to solve this problem, so don't worry if you attacked this problem from a different angle. This following method avoids using the quadratic formula:

First, we will calculate how long it takes for the ball to travel upward, and then come back down to its original height. 

Since we are neglecting air resistance, we know that our final velocity is equal but in the opposite direction as the initial velocity. Therefore, we get:

At this point, the ball is at it's original height of , but traveling downward at a rate of .

We can then use the following expression to calculate the velocity of the ball as it hits the ground:

Plugging in our values:

Then using our original expression again:

Adding our times together:

For this problem, the following kinematic equation is necessary:

Since the plane starts at rest, we can simplify the equation to

The problem defines the acceleration to be  and the time to be  seconds so

First we convert our units to SI,  feet is  meters and  minutes is  seconds. Now we combine this dividing  by  to arrive at our average velocity of 

Since the pine cone starts from rest and we are given a distance we will use: 

. 

Solving for t:

*Note that the distance is negative since the object is falling and gravitational acceleration is downward. One could also just ignore the signs since time cannot be negative.

Since the stone is dropped from rest and we are searching for a distance, we can use the kinematic equation :.

We can eliminate the second term, initial velocity times time because the stone is dropped.

But since the mine shaft is filled with 5 meters of water its actual depth would 130 meters.

The projectile started from rest and we are given its initial velocity, the muzzle velocity that is. Use the kinematic equation: .

The initial velocity is canceled out:

Solve for a:

Use the kinematic equation . Note that the grasshoppers final speed will be equal to 0.

Square rooting both sides:

The Earth's gravitational acceleration is approximately  while the acceleration of gravity on the Moon is about 1.6. In other words the Earth's pull is much stronger than the Moon's. Objects will fall faster here on Earth.

Gravity is the same at all heights with minor exceptions over great distances such as deep in the Earth and at 30,000 feet; gravity would be stronger that much closer to Earth. 

Acceleration of gravity pulls everything downward- all the time and even if an object isn't moving. So acceleration and velocity can't always point in the same direction as the stones initial velocity points up.

The time traveling up will be equal to time falling as the motions just cancel each other. Gravity is slowing the stone as it travels upward until it stops very, very briefly and begins to accelerate and travel downward.