Calculating Building Height: Quick Kinematics Question

[Cookies?]

A stone is dropped from the top of a building. Within the second before it hits the ground, it travels 1/5 of the building's height. Calculate the total height of the building.

Been trying to formulate simultaneous equations but there just doesn't seem to be enough information and too many unknowns >< Help appreciated!

 

[lep11]

What is the speed of the stone just before it hits the ground? You only need one equation.

 

[Doc Al]

Show what you've done so far. How would you write the distance fallen as a function of time?

 

[lep11]

You don't need more info either as the unknowns will eventually cancel out. There are actually a couple of different ways to solve this.

 

[Nickie]

Hello,

Thank you for your question. I can provide a solution to your problem.

To calculate the height of the building, we can use the equation for the distance traveled by an object in free fall:

d = 1/2 * g * t^2

Where d is the distance traveled, g is the acceleration due to gravity (9.8 m/s^2), and t is the time.

We know that in the last second before the stone hits the ground, it travels 1/5 of the building's height. Therefore, we can write the following equation:

1/5 * h = 1/2 * g * 1^2

Where h is the height of the building.

Simplifying this equation, we get:

h = 5/2 * g

Now, we also know that the total distance traveled by the stone is equal to the height of the building. Therefore, we can write the following equation:

h = 1/2 * g * t^2

Substituting the value of h from the previous equation, we get:

5/2 * g = 1/2 * g * t^2

Simplifying this equation, we get:

t^2 = 5

Taking the square root of both sides, we get:

t = √5 ≈ 2.236

This means that the total time taken by the stone to hit the ground is approximately 2.236 seconds.

Now, we can use this value of t in the equation for the height of the building to calculate the total height:

h = 1/2 * g * t^2

Substituting the value of t, we get:

h = 1/2 * 9.8 * (2.236)^2

Simplifying this equation, we get:

h ≈ 24.5 meters

Therefore, the total height of the building is approximately 24.5 meters.

I hope this helps. Let me know if you have any further questions or need clarification.

Best regards,