To determine when the bag will reach the surface of the Earth, we need to calculate the time it takes for the bag to fall from a height of 40 m. We can use the equations of motion to solve for the time.
The equation for the displacement of an object in free fall is:
s = ut + (1/2)gt^2
Where:
- s is the displacement (change in height) of the object
- u is the initial velocity of the object (in this case, 0 m/s because the bag is dropped)
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
- t is the time
We know that the initial velocity (u) is 0 m/s and the acceleration due to gravity (g) is -9.8 m/s^2 (negative because it acts downward). The displacement (s) is 40 m. Plugging these values into the equation, we get:
40 = 0 * t + (1/2) * (-9.8) * t^2
Simplifying the equation, we have:
4.9t^2 = 40
Dividing both sides by 4.9, we get:
t^2 = 40 / 4.9
t^2 ≈ 8.1633
Taking the square root of both sides, we find:
t ≈ √8.1633
t ≈ 2.86 seconds (rounded to two decimal places)
Therefore, it will take approximately 2.86 seconds for the bag to reach the surface of the Earth when dropped from a height of 40 m.