a rock is dropped from a height of 20m above the ground when it hits the ground it leaves a hole 10cm deep with what speed does the rock hit the ground, and what is the magnitude of the rock's deceleration after it hits the ground
v = √(2as) = √(2*9.8*20) = 19.80 m/s
Now use that to answer the other question.
To determine the speed at which the rock hits the ground, you can use the equation for free-fall motion. The equation relates the distance fallen by an object to its initial velocity, acceleration due to gravity, and time taken to fall.
Let's start by finding the time it takes for the rock to fall. We can use the equation for the distance fallen during free fall:
d = 1/2 * g * t^2
Given that the rock is dropped from a height of 20m, we can substitute d = 20m and the acceleration due to gravity, g = 9.8 m/s^2.
20m = 1/2 * 9.8 m/s^2 * t^2
Simplifying the equation,
t^2 = (20m * 2) / (9.8 m/s^2)
t^2 = 40s^2 / 9.8 m/s^2
t^2 ≈ 4.08s^2
Taking the square root of both sides, we find:
t ≈ 2.02 seconds
So, it takes approximately 2.02 seconds for the rock to fall.
Next, we can calculate the speed at which the rock hits the ground. We can use the equation:
v = g * t
Substituting the value of acceleration due to gravity, g = 9.8 m/s^2, and the time taken, t ≈ 2.02 seconds:
v = 9.8 m/s^2 * 2.02s
v ≈ 19.8 m/s
Therefore, the speed at which the rock hits the ground is approximately 19.8 m/s.
To determine the magnitude of the rock's deceleration after it hits the ground and creates a hole, we need to consider the change in speed and the time taken to come to a stop. The rock slows down due to a deceleration force, which is equal to the acceleration but in the opposite direction.
The change in speed can be calculated as the initial speed subtracted from the final speed:
Change in speed = Initial speed - Final speed
As the rock comes to rest, the final speed will be zero. So, the change in speed is equal to the initial speed:
Change in speed = 19.8 m/s
To find the magnitude of the rock's deceleration, we divide the change in speed by the time taken for the deceleration:
Deceleration = Change in speed / Time taken
Given that the time taken for the deceleration is not provided in the question, we can't find the exact value for the deceleration. Without additional information, we can't determine the magnitude of the rock's deceleration.