To determine the time it takes for a stone to come back down when thrown vertically upwards, we need to consider the motion of the stone under the influence of gravity.
When the stone is thrown upwards, it experiences an initial velocity (let's call it "v0") in the upward direction. As it moves upwards, gravity acts as a decelerating force, gradually reducing its velocity until it reaches its highest point (the highest point is where the stone momentarily comes to rest before reversing its direction).
At the highest point, the stone's velocity becomes zero, and then gravity starts to accelerate it downwards. The time it takes for the stone to reach its highest point is equal to the time it takes for the stone to come back down to the surface of the Earth.
We can calculate the time it takes for the stone to reach the highest point using the following formula:
Time to highest point = (Final velocity - Initial velocity) / Acceleration
Since the final velocity at the highest point is zero, the formula simplifies to:
Time to highest point = -v0 / g
Where:
- v0 is the initial velocity of the stone
- g is the acceleration due to gravity (approximately 9.8 m/s² on Earth)
After reaching the highest point, the stone will take the same amount of time to fall back to the surface of the Earth. So, the total time of flight can be calculated as:
Total time of flight = 2 * (Time to highest point)
It's important to note that this calculation assumes no air resistance, and we consider the acceleration due to gravity to be constant. In reality, factors like air resistance may slightly affect the stone's motion.