A bomb dropped from a balloon reaches the ground in 30seconds .determine the height of the balloon if it is at rest in the air and if it is ascending with a speed of 100m/sec when the balloon is dropped
if Vi = 0
h = Hi + 0 t - 4.9 t^2
h = 0 at ground
4.9 t^2 = Hi
4.9 * 900 = Hi
=================
if Vi = 100
0 = Hi + 100 t - 4.9 t^2
Hi = 4.9 * 900 - 3000
To determine the height of the balloon, we can use the basic equations of motion. Let's denote the height of the balloon as "h," and the time it takes to reach the ground as "t."
When the balloon is at rest in the air, it is not moving vertically. So we can assume its initial velocity, "u," is zero. The acceleration due to gravity, "g," is downward and is approximately 9.8 m/s².
Using the equation of motion, h = ut + (1/2)gt², we can substitute the values:
h = 0 + (1/2)(9.8)(30)²
h = 0 + (1/2)(9.8)(900)
h = 0 + 4.9(900)
h = 4410 meters
Therefore, when the balloon is at rest in the air, the height of the balloon is 4,410 meters.
Now let's consider the scenario where the balloon is ascending with a speed of 100 m/s when the balloon is dropped. In this case, the initial velocity, "u," is 100 m/s, and we can assume that the acceleration due to gravity remains the same.
Using the same equation of motion, h = ut + (1/2)gt², we can substitute the values:
h = 100(30) + (1/2)(9.8)(30)²
h = 3000 + (1/2)(9.8)(900)
h = 3000 + 4.9(900)
h = 3000 + 4410
h = 7410 meters
Therefore, when the balloon is ascending with a speed of 100 m/s when the balloon is dropped, the height of the balloon is 7,410 meters.
To determine the height of the balloon when it is at rest in the air, we can use the formula for free fall:
h = (1/2) * g * t^2
where:
h is the height
g is the acceleration due to gravity (9.8 m/s^2)
t is the time (30 seconds)
Plugging in the values, we have:
h = (1/2) * 9.8 m/s^2 * (30 s)^2
h = (1/2) * 9.8 m/s^2 * 900 s^2
h = 4410 m
Therefore, the height of the balloon when it is at rest in the air is 4410 meters.
Now, let's determine the height of the balloon if it is ascending with a speed of 100 m/s when the balloon is dropped.
For this case, we can use the equation of motion:
h = h0 + v0t + (1/2)at^2
where:
h is the height
h0 is the initial height (unknown)
v0 is the initial upward velocity (100 m/s)
t is the time (30 seconds)
a is the acceleration due to gravity (-9.8 m/s^2)
Since the balloon is dropped, the initial height (h0) is zero. Plugging in the values, we have:
h = 0 + 100 m/s * 30 s + (1/2) * (-9.8 m/s^2) * (30 s)^2
h = 3000 m - 4410 m
h = -1410 m
Therefore, the height of the balloon when it is ascending with a speed of 100 m/s when the balloon is dropped is -1410 meters. This means it would have reached a height of -1410 meters above the starting point.