# If a stone is dropped at an altitude of 174.9 m from a helicopter which is ascending with a velocity of 20.68 m/s, how long does the stone take to reach the ground?

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The problem I am having is that I am confused about using **positive** #g# because gravity is directed towards the Earth and the stone is falling in that direction or if I should be using **negative** #g# because the stone is falling opposite to the direction in which the helicopter is ascending, upwards??

It would really help if you guys could explain why g should be negative or positive. Thanks guys. :))

The problem I am having is that I am confused about using **positive** **negative**

It would really help if you guys could explain why g should be negative or positive. Thanks guys. :))

8.45 seconds.

We can look at this much more closely by starting from scratch with Newton's second law. When the stone is dropped it has an initial velocity but the only force acting on it is due to gravity. We have defined upwards as the positive y direction so by Newton's second law we can write

This is because the stone will accelerate towards the earth, which we have defined as the negative direction.

Integrating this expression gives:

This models the velocity and makes sense if you think about it. When it's released, it will have the same velocity as the helicopter and will thus move upwards for a time but as time progresses it will stop and then begin to fall.

To find displacement, we integrate again:

This is definitely a job for the quadratic formula:

We discard the negative solution so therefore the stone takes 8.45 seconds to hit the ground.

Now use

Now we don't have any pesky initial velocities to contend with, just a straight fall from this height:

As upwards is positive, falling will result in a negative displacement so

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8.45s

Using the point of origin—the stone dropped from the helicopter—we move forward as follows:

Downward acceleration (g) and downward displacement (h) should be interpreted as negative if the upward initial velocity is assumed to be positive.

Calculating the time (t) to reach the ground now

Thus, we have

When we combine these with the variables h, u, g, and t in the equation of motion under gravity, we obtain

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The time it takes for the stone to reach the ground can be calculated using the following formula: [ \text{Time} = \sqrt{\frac{2 \times \text{Altitude}}{\text{Acceleration due to gravity}} + \frac{\text{Initial velocity}^2}{(\text{Acceleration due to gravity})^2}} ] Substitute the given values: [ \text{Time} = \sqrt{\frac{2 \times 174.9}{9.8} + \frac{20.68^2}{9.8^2}} ]

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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