Final answer:
The stone takes approximately 4.08 seconds to reach the ground.
Step-by-step explanation:
To calculate the time it takes for the stone to reach the ground, we need to analyze its vertical motion. When the stone is thrown upwards, it follows a parabolic path before falling back down.
The key to solving this problem is to find the time it takes for the stone to reach its maximum height, and then double that value to find the total time of flight.
First, we can use the initial vertical velocity of the stone (20 m/s) and the acceleration due to gravity (-9.8 m/s^2) to calculate the time it takes for the stone to reach its maximum height. We use the equation:
vy = v0y + gt
where vy is the final vertical velocity (0 m/s at maximum height), v0y is the initial vertical velocity (20 m/s), g is the acceleration due to gravity (-9.8 m/s^2), and t is the time taken.
Plugging in these values, we get:
0 = 20 + (-9.8)t
9.8t = 20
t = 20 / 9.8
t ≈ 2.04 s
Doubling this time will give us the time of flight:
Time of flight = 2 * 2.04 s
Time of flight ≈ 4.08 s
Therefore, it takes approximately 4.08 seconds for the stone to reach the ground.