A 124- balloon carrying a 22- basket is descending with a constant downward velocity of 27.4 A 1.0- stone is thrown from the basket with an initial velocity of 20.0 perpendicular to the path of the descending balloon, as measured relative to a person at rest in the basket. The person in the basket sees the stone hit the ground 5.20 after being thrown. Assume that the balloon continues its downward descent with the same constant speed of 27.4 .How high was the balloon when the rock was thrown out?
To find the height of the balloon when the rock was thrown out, we can use the following steps:
Step 1: First, let's determine the time it takes for the stone to hit the ground as observed from the person in the basket. We are given that the stone hits the ground 5.20 s after being thrown.
Step 2: The vertical motion of the stone is affected by gravity. We can use the equation for vertical motion to find the time it takes for the stone to hit the ground.
Step 3: The equation for vertical motion is given by:
d = v₀t + (1/2)gt²
Where:
d is the vertical distance traveled (downward),
v₀ is the initial vertical velocity of the stone (0 m/s),
t is the time it takes for the stone to hit the ground,
g is the acceleration due to gravity (-9.8 m/s²).
Step 4: Substituting the given values into the equation, we have:
0 = 0 + (1/2)(-9.8)t²
Step 5: Solving for t, we get:
t = sqrt(0 - 2 * (0.5)(-9.8)t²) / (-9.8)
Step 6: Simplifying the equation, we have:
t = sqrt(9.8t²) / 9.8
Step 7: Simplifying further, we have:
t = sqrt(t²)
Since time cannot be negative, we can ignore the negative solution.
Step 8: Simplifying the equation, we get:
t = t
This implies that t = 0, which means the stone was thrown at the same time as it hit the ground. However, this contradiction indicates that our initial assumption was incorrect.
Therefore, it is not possible for the person in the basket to observe the stone hitting the ground after being thrown. Please check the given information and assumptions for any inconsistencies.
To find the height of the balloon when the rock was thrown out, we can use the following steps:
Step 1: Determine the time it takes for the stone to hit the ground after being thrown.
We are given that the person in the basket sees the stone hit the ground 5.20 seconds after being thrown.
Step 2: Calculate the distance traveled by the stone horizontally.
Since the stone was thrown perpendicular to the path of the descending balloon, it only travels horizontally. The horizontal distance traveled by the stone can be determined using the formula:
distance = velocity x time
The velocity of the stone is given as 20.0 m/s, and we have already determined that the time is 5.20 seconds.
Step 3: Calculate the initial height of the balloon.
The initial height of the balloon can be calculated using the formula for free-fall motion:
initial height = final height - 0.5 x g x t^2
where g is the acceleration due to gravity and t is the time it takes for the stone to hit the ground.
In this case, the final height is zero, as the stone hits the ground. The acceleration due to gravity (g) is approximately 9.8 m/s^2.
Substitute the values into the formula to find the initial height of the balloon.
initial height = 0 - 0.5 x 9.8 x (5.20)^2
After performing the calculation, the initial height of the balloon would be determined.