if a rock has 25kg of mass and the height of the fall is 78.4 how long will it tale to hit the ground
To determine how long it will take for a rock to hit the ground when it is dropped from a certain height, you can use the equation of motion for an object under constant acceleration due to gravity, assuming there is no air resistance.
The equation of motion is:
\[ h = \frac{1}{2} g t^2 \]
where:
- \( h \) is the height from which the rock is dropped (78.4 meters in your case),
- \( g \) is the acceleration due to gravity (approx. \( 9.81 \, m/s^2 \) on Earth),
- \( t \) is the time in seconds.
Rearrange the formula to solve for \( t \):
\[ t = \sqrt{\frac{2h}{g}} \]
Now plug in the numbers:
\[ t = \sqrt{\frac{2 \times 78.4 \, m}{9.81 \, m/s^2}} \]
\[ t = \sqrt{\frac{156.8 \, m}{9.81 \, m/s^2}} \]
\[ t = \sqrt{15.9878 \, s^2} \]
\[ t \approx 4 \, s \]
So, it will take approximately 4 seconds for the rock to hit the ground.
The mass of the rock does not affect the time it takes to hit the ground in a vacuum, because all objects accelerate at the same rate under gravity when there is no air resistance. However, in the real world, the shape and air resistance will play a role, but since the problem does not provide information on these factors, we can't account for them in the calculation.