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 the initial height of the balloon to the ground. We can use the equations of motion to solve this problem.
Given: Initial height (h) = 40 m Initial velocity (u) = 10 m/s (upwards) Acceleration due to gravity (g) = 9.8 m/s² (downwards)
We can use the equation of motion to find the time it takes for the bag to fall:
h = ut + (1/2)gt²
Substituting the given values:
40 = (10)t + (1/2)(9.8)t²
Rearranging the equation and simplifying:
4.9t² + 10t - 40 = 0
We can solve this quadratic equation using the quadratic formula:
t = (-b ± √(b² - 4ac)) / (2a)
In this case, a = 4.9, b = 10, and c = -40. Plugging these values into the formula:
t = (-10 ± √(10² - 4(4.9)(-40))) / (2(4.9))
t = (-10 ± √(100 + 784)) / 9.8
t = (-10 ± √884) / 9.8
Now we can calculate the time taken for the bag to fall:
t₁ = (-10 + √884) / 9.8 ≈ 1.92 seconds
t₂ = (-10 - √884) / 9.8 ≈ -4.07 seconds (we disregard the negative value)
Therefore, the bag will reach the surface of the Earth approximately 1.92 seconds after being dropped from the balloon.