Calculate depth of fall.

if stone fells 10 sec into a pit, how deep is it?

Great, let's work through this problem together! To start, can you tell me what you know about the motion of objects falling under gravity and how that might relate to the problem? Also, have you made any attempts to solve it yet?

V=g*t and g=9.81m/s^2

Excellent, you've identified the key concept correctly. The velocity ( V ) of an object falling under gravity can be calculated using ( V = g \times t ), where ( g ) is the acceleration due to gravity (approximately ( 9.81 , \text{m/s}^2 )) and ( t ) is the time in seconds.

However, to find the depth of the pit, we need to calculate the distance the stone travels in that time. The formula you mentioned gives us the velocity at a specific moment (after 10 seconds in this case), not the total distance traveled.

Do you know the formula to calculate the distance an object falls under gravity over a certain period of time?

What formula do I need for the deep?

For calculating the depth of the pit, which is the distance the stone travels as it falls, you need to use a different formula. The correct formula for the distance ( d ) an object travels when falling under gravity for a time ( t ) is:

[ d = \frac{1}{2} g t^2 ]

Here, ( g ) is the acceleration due to gravity (approximately ( 9.81 , \text{m/s}^2 )), and ( t ) is the time in seconds. This formula assumes that the initial velocity is zero, which fits our scenario as the stone is initially at rest.

Can you try using this formula to calculate the depth of the pit? The time ( t ) given in your problem is 10 seconds.

d = 0.59.8110^2 = 490.5 m

That's exactly right! You've applied the formula correctly. By substituting the values into the formula ( d = \frac{1}{2} g t^2 ), you get:

[ d = \frac{1}{2} \times 9.81 \times 10^2 = 490.5 , \text{meters} ]

So, the depth of the pit is 490.5 meters. Great job on solving the problem!

Based on your approach and accuracy, I would grade your work as an A. You understood the concept, applied the right formula, and calculated the answer correctly. Keep up the good work!