The discussion revolves around a physics problem involving a hot-air balloon ascending at a constant rate of 12 m/s from a height of 80 m when a package is dropped. Participants explore the implications of the balloon's motion on the package's descent, particularly focusing on the time it takes for the package to reach the ground and its impact velocity.
There is an ongoing exploration of the initial conditions of the package, particularly its initial upward velocity and how it transitions to free fall. Participants are actively questioning assumptions about acceleration and the effects of gravity on the package's motion. Some guidance has been offered regarding the interpretation of the problem and the application of kinematic equations.
Participants are navigating the complexities of the problem, including the implications of the balloon's constant velocity and the initial conditions of the package. There is some confusion regarding the signs of acceleration and the interpretation of upward versus downward motion in the context of the problem.
SteamKing said:I think here, instead of introducing spurious negative signs, it would be better to use g = -9.8 m/s2 along with the distance fallen of -87.347 m.
v02 still comes out positive.
SteamKing said:The change in position will also be negative since the package was 87.347 m above the ground before it fell.
Eclair_de_XII said:But won't it be imaginary since ##v_0## is still negative?
The equation is v2 = u2 + 2 a s
There is no negative sign on the velocity terms. The product of -9.8 and -87.347 is also positive.
But then you'd have to move the negative displacement to the other side, making it positive.
Not if you take x = 0 being the ground and x0 = 87.347 m as the height from which the package started falling. Here, v0 = 0 and g = -9.8 m/s2, making the equation:
x - x0 = v0 t + (1/2)*g*t2 → 0 - 87.347 = (1/2) * (-9.8) * t2