A person holding a lunch bag is moving upward in a hot air balloon at a constant speed of 6.6 m/s . When the balloon is 24 m above the ground, she accidentally releases the bag.
To calculate the time it takes for the lunch bag to hit the ground after being released, we can use the equation for free-falling objects. The equation is:
d = 1/2 * g * t^2
Where:
- d is the distance the lunch bag falls.
- g is the acceleration due to gravity (approximately 9.8 m/s^2).
- t is the time it takes for the lunch bag to reach the ground.
In this case, the initial velocity of the lunch bag is 0 m/s because it was released while the person holding the bag was moving at a constant speed upwards. The acceleration due to gravity will cause the lunch bag to fall downwards.
First, let's calculate the time it takes for the person to reach a height of 24 m:
d = v * t
24 m = 6.6 m/s * t
Solving for t, we have:
t = 24 m / 6.6 m/s
t ≈ 3.64 seconds
Now, we can use this time to calculate how far the lunch bag falls:
d = 1/2 * g * t^2
d = 1/2 * 9.8 m/s^2 * (3.64 s)^2
d ≈ 66.19 meters
Therefore, the lunch bag falls approximately 66.19 meters from the moment it is released until it reaches the ground.