To calculate the height of an object that is pushed off a cliff or table, given the time taken before it hits the ground and the initial velocity, you can use the following equation of motion:
h = v₀t + (1/2)gt²
Where:
- h is the height of the object.
- v₀ is the initial velocity (upward or downward) of the object.
- t is the time taken for the object to hit the ground.
- g is the acceleration due to gravity (approximately 9.8 m/s² on Earth).
To use this equation, you need to consider the direction of the initial velocity. If the object is thrown upward with an initial velocity v₀, it will reach its highest point before falling back down. In this case, the height you calculate will be the maximum height reached by the object.
If the object is simply dropped or pushed downward with an initial downward velocity, the height calculated will be the distance from the starting point to the ground.
Make sure to use consistent units for all the variables (e.g., meters for height, seconds for time, meters per second for velocity) to obtain accurate results.