What is the velocity of an object that is dropped from a height of 20m,just before it reaches the ground?
vf^2=2(g)Height
solve for vf
14.14
To determine the velocity of an object just before it reaches the ground when dropped from a certain height, you can use the principles of physics and apply the equations of motion.
In this scenario, the object is dropped from a height of 20m, meaning it falls freely under the influence of gravity. Here's how you can calculate its velocity:
Step 1: Identify the known values:
- Initial height (h) = 20m
- Acceleration due to gravity (g) = 9.8 m/s² (approximately)
Step 2: Use the equation of motion for vertical motion:
The equation for displacement with constant acceleration is:
s = ut + (1/2)at²
In this case, the initial velocity (u) is zero since the object is dropped and the final displacement (s) is -20m (negative since it is in the downward direction). The equation can be rearranged as:
s = ut + (1/2)at²
-20 = 0t + (1/2)(-9.8)t²
Step 3: Solve the equation:
-20 = -4.9t²
Step 4: Calculate the time (t):
Divide both sides by -4.9:
t² = 20/4.9
t ≈ √(20/4.9)
t ≈ √4.0816
t ≈ 2.02 seconds (rounded to two decimal places)
Step 5: Calculate the final velocity (v):
Use the equation of motion:
v = u + at
v = 0 + (9.8)(2.02)
Step 6: Calculate the final velocity:
v ≈ 19.796 m/s (rounded to three decimal places)
Therefore, when an object dropped from a height of 20m is just about to reach the ground, its velocity will be approximately 19.796 m/s directed downward.