A person holding a lunch bag is moving upward in a hot air balloon at a constant speed of 6.1 m/s . When the balloon is 28 m above the ground, she accidentally releases the bag.

What is the speed of the bag just before it reaches the ground?

I got Vf^2= Vo^2 +2ad
Vf^2= 0+ (2*9.8) *28 = 548.8
Vf= Squareroot 548.8 = 23.4

But that answer is not correct. Can you please help me find my mistake and the right answer? THANK YOU!!!!!

It seems that you have made a calculation mistake in your equation. The equation you used, Vf^2 = Vo^2 + 2ad, is the correct formula to calculate the final velocity of an object in free fall.

Given that the initial velocity (Vo) is 0 (since the lunch bag was released), the acceleration (a) is -9.8 m/s^2 (taking gravity as the only force acting on the bag), and the displacement (d) is 28 m, you can substitute these values into the equation to find the final velocity (Vf) of the bag.

Vf^2 = 0^2 + 2(-9.8)(28)
Vf^2 = 0 + (-19.6)(28)
Vf^2 = -548.8

Upon solving this equation, you arrived at Vf = 23.4 m/s, which is almost correct. However, the negative sign in the equation indicates that the velocity is in the opposite direction to the initial direction. In this case, since the bag was released while moving upward, the final velocity should also be negative.

Therefore, the correct final velocity of the bag just before it reaches the ground is -23.4 m/s.

To find the speed of the bag just before it reaches the ground, you correctly used the equation Vf^2 = Vo^2 + 2ad, where Vf is the final velocity, Vo is the initial velocity, a is the acceleration, and d is the distance traveled.

However, a common mistake made in this problem is assuming that the initial velocity (Vo) is zero. In this case, the initial velocity of the bag is the same as the person's upward speed in the hot air balloon, which is given as 6.1 m/s. Therefore, your equation should be:

Vf^2 = (6.1)^2 + 2(9.8)(28)

Calculating this equation, we get:

Vf^2 = 37.21 + 548.8
Vf^2 = 586.01

Taking the square root of both sides, we find:

Vf = √586.01
Vf ≈ 24.2 m/s

So the correct answer is approximately 24.2 m/s.

24.207676m/s is what I got for the speed. That number negative would be the velocity.