Calculate Height of Falling Stone: 2.2m Window in 0.28s

• jena
In summary, the question asks for the height from which a stone fell if it takes 0.28 seconds to travel past a window 2.2 meters tall. Using the formula y=(v^2-V(i)^2)/2a, with a being -9.8 m/s^2, we can solve for the height to be 3.46 meters. However, after further clarification and rearranging the formula, the correct height is actually 2.15 meters.
jena
Hi,
I have a question about height and a falling stone. The question reads:

Question: A stone falling takes 0.28 seconds to travel past a window 2.2 meters tall. From what height above the tope of the window did the stone fall?

Thank You

How did you do it?

Daniel.

i.e. show your work if you want help.

heh, i remember doing that problem out of giancoli years ago.

Work

Sorry here's my work.
Work:

t=0
y(i)=0
v=0
V(i)=7.86 m/s
a= -9.8 m/s^2

y= (v^2-V(i)^2)/2a

y=(0-(7.86)^2)/(2*.9.8)

y=3.46 m

Thank You

jena said:
Sorry here's my work.
Work:

t=0
y(i)=0
v=0
V(i)=7.86 m/s
a= -9.8 m/s^2

What do you denote by v(i) and how did you derived it? If you mean the speed at the top of the window I assume you found it as:

$$v_i = \frac{h - \frac{gt^2}{2}}{t}$$,

Its value should be 6.49 m/s instead.

Also do not consider accelearation as negative. It is easier to take the y-axis pointing downward to make all vector quantities positive.

jena said:
y= (v^2-V(i)^2)/2a

y=(0-(7.86)^2)/(2*.9.8)

y=3.46 m

Thank You

Almost there, but you need to arrange a little, as v_i is actually the final velocity for the part of the trajectory from drop point to the top of the window. So,

$$h = \frac{v_i^2}{2g}$$

You should get a value of 2.15 m.

Last edited:
Thank you, I see where I got confused

1. How do you calculate the height of a falling stone using the given information?

To calculate the height of a falling stone, you can use the formula h = 1/2 * g * t^2, where h is the height, g is the acceleration due to gravity (usually 9.8 m/s^2), and t is the time. In this case, we have h = 1/2 * (9.8 m/s^2) * (0.28 s)^2 = 0.3836 m. Therefore, the height of the falling stone is 0.3836 meters or 38.36 centimeters.

2. Why is the time of 0.28 seconds used in the calculation?

The time of 0.28 seconds is used in the calculation because it is the amount of time it took for the stone to fall past the window. This is known as the "time of flight" and is a crucial piece of information needed to calculate the height of the falling stone.

3. Is the acceleration due to gravity always 9.8 m/s^2?

Yes, the acceleration due to gravity is usually considered to be 9.8 m/s^2. However, this value can vary slightly depending on factors such as altitude and location on Earth. In this calculation, we have used the standard value of 9.8 m/s^2.

4. Can this formula be used for any falling object, not just a stone?

Yes, this formula can be applied to any object that is falling due to the force of gravity. However, it is important to note that other factors such as air resistance may affect the accuracy of the calculation for objects other than stones.

5. How accurate is this calculation in determining the height of the falling stone?

This calculation is accurate in determining the approximate height of the falling stone. However, it may not be completely accurate due to factors such as air resistance and the presence of other external forces. Additionally, the precision of the time measurement may also affect the accuracy of the calculation.

Replies
4
Views
7K
Replies
4
Views
25K
Replies
25
Views
819
Replies
23
Views
2K
Replies
3
Views
9K
Replies
10
Views
4K
Replies
1
Views
1K
Replies
1
Views
1K
Replies
2
Views
1K
Replies
13
Views
1K