Calculate the velocity of an object that falls from a height of 50 meters, ignoring air resistance
Answers:
To calculate the velocity of an object falling from a height of 50 meters while ignoring air resistance, we can use the equations of motion under uniform acceleration due to gravity. The relevant equation is:
[ v^2 = u^2 + 2gh ]
Where:
- ( v ) is the final velocity,
- ( u ) is the initial velocity (which is 0 for an object starting from rest),
- ( g ) is the acceleration due to gravity (approximately ( 9.81 , \text{m/s}^2 )),
- ( h ) is the height (50 meters in this case).
Since the object starts from rest, we have ( u = 0 ). Plugging in the values:
[ v^2 = 0 + 2 \cdot 9.81 \cdot 50 ]
Calculating the right-hand side:
[ v^2 = 2 \cdot 9.81 \cdot 50 = 981 ]
Now, take the square root to find ( v ):
[ v = \sqrt{981} \approx 31.33 , \text{m/s} ]
Hence, the velocity of the object just before it hits the ground is approximately 31.33 m/s.