A rock is dropped from a height of 4m. How long does it take to reach the ground
h = 0.5g*T^2 = 4
4.9T^2 = 4
T = 0.90 s.
Well, if the rock were to take a break and enjoy a cup of tea on the way down, it would probably take quite a while. But since gravity isn't very patient, the rock falls at a rate of 9.8 meters per second squared. Using a handy dandy physics formula, we can calculate that it takes approximately 0.9 seconds for the rock to reach the ground. However, keep in mind that this calculation doesn't account for factors like air resistance or the rock's desire to join a rock band and travel the world, so take it with a grain of salt...or in this case, a grain of rock.
To find the time it takes for a rock to reach the ground when dropped from a height of 4m, we can use the equation of motion:
s = ut + (1/2)gt^2
Where:
s = final position (in this case, 0m since it reaches the ground)
u = initial velocity (0m/s as it is dropped, there is no initial velocity)
t = time taken
g = acceleration due to gravity (-9.8m/s^2)
Plug in the values we know:
0 = (0 * t) + (1/2)(-9.8)(t^2)
Simplifying the equation:
0 = -4.9t^2
Since there is only one unknown variable (t), we can solve for it by rearranging the equation:
t^2 = 0 / -4.9
t^2 = 0
Therefore, t = 0.
Based on this calculation, it appears that the rock will reach the ground instantly. However, this is not possible in reality as there are factors (such as air resistance) that will cause the rock to take some time to reach the ground. In our calculation, we have neglected these factors to simplify the equation. The actual time for the rock to reach the ground will be very small but not instantaneous.
To find the time it takes for the rock to reach the ground, we can use the laws of motion and the formula for free fall.
The formula for calculating the time it takes for an object to fall freely from a given height (h) can be derived from the equation of motion: s = ut + 0.5 * a * t^2. In this equation:
- s represents the distance traveled (in meters),
- u represents the initial velocity of the object (which is zero when the object is dropped from rest),
- a represents the acceleration due to gravity (approximately 9.8 m/s^2 on Earth), and
- t represents the time taken (in seconds).
In this case, the distance traveled (s) is equal to the height from which the rock was dropped (4m). The initial velocity (u) is zero, as the rock is dropped from rest. The acceleration due to gravity (a) is approximately 9.8 m/s^2.
Plugging these values into the formula, we have:
4 = 0 + 0.5 * 9.8 * t^2
To solve for t, we can rearrange the equation:
4 = 4.9 * t^2
Dividing both sides by 4.9:
t^2 = 0.816
Taking the square root of both sides:
t ≈ 0.904
Therefore, it takes approximately 0.904 seconds for the rock to reach the ground when dropped from a height of 4 meters.