To determine the time it takes for the rock to hit the ground and its velocity at impact, we can use basic physics equations related to free-fall motion. Assuming no air resistance, we can use the following equations:
The equation for calculating the time it takes for an object to fall from a certain height h is given by:
t = √(2h/g),
where t represents time, h is the height, and g is the acceleration due to gravity (approximately 9.8 m/s² on Earth).
The final velocity (v) of an object in free fall can be calculated using the equation:
v = gt,
where g is the acceleration due to gravity and t is the time of fall.
Let's apply these equations to solve the problem:
Given: Height (h) = 6 m Acceleration due to gravity (g) = 9.8 m/s²
- Time to reach the ground (t): t = √(2h/g) t = √(2 * 6 / 9.8) t ≈ 0.88 seconds (rounded to two decimal places)
Therefore, it takes approximately 0.88 seconds for the rock to hit the ground.
- Velocity at impact (v): v = gt v = 9.8 * 0.88 v ≈ 8.63 m/s (rounded to two decimal places)
Hence, the velocity of the rock as it hits the ground is approximately 8.63 m/s.