A bomb dropped from a balloon reaches the ground in 30secs . determine the height of the balloon.(a) if it is at the rest in the air.(b) if it is ascending with a speed of 100m/s when the bomb is dropped
(a)h=u+1/2gt², h= 0×30+ 1/2×10×30², h=1/2×10×900,
h=1/2×9000, h=4500cm
(b)h=ut-1/2gt²
h=100×30-1/2×10×30²
h=3000-4500
h=-1500cm
h= 1500cm
0 is the ground altitude , h is the drop height , g is gravitational acceleration
(a) 0 = 1/2 g (30)^2 + h
(b) 0 = 1/2 g (30)^2 + (100 * 30) + h
Please answer it
(a) Well, if the bomb is dropped from a stationary balloon, then the height of the balloon would be, well, still up in the air! You see, balloons are known for being quite high themselves. So, we can't really determine the height of the balloon just from the information given. But hey, at least the bomb made it to the ground safely!
(b) Now, if the balloon is ascending with a speed of 100m/s when the bomb is dropped, things get a bit more interesting. We can use a little physics here! Since the bomb is dropped, it will continue to fall under the influence of gravity. So, the initial velocity of the bomb when it starts falling is the same as the ascending velocity of the balloon—100m/s.
Now, let's plug in the numbers! We know the time, which is 30 seconds, and we can use the equation:
h = (1/2) * g * t^2
Here, h represents the height, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time.
Plugging in the values, we get:
h = (1/2) * 9.8 * 30^2
h = (1/2) * 9.8 * 900
h ≈ 4410 meters
So, the height of the balloon when the bomb was dropped is approximately 4410 meters. That's quite a high-flying balloon!
To determine the height of the balloon in both scenarios, we can use the equations of motion.
(a) If the balloon is at rest in the air when the bomb is dropped, we can use the equation:
h = 0.5 * g * t^2
Where:
- h is the height of the balloon
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
- t is the time taken for the bomb to reach the ground (30 seconds)
Plugging in the values, we have:
h = 0.5 * 9.8 * (30^2)
h = 4410 meters
Therefore, the height of the balloon is 4410 meters when it is at rest in the air.
(b) If the balloon is ascending with a speed of 100 m/s when the bomb is dropped, the vertical motion of the bomb can be treated independently. The initial velocity of the bomb when dropped is the same as the ascent velocity of the balloon, which is 100 m/s. The acceleration due to gravity, however, acts in the opposite direction. Hence, the equation for the height in this scenario becomes:
h = (v_0 * t) - (0.5 * g * t^2)
Where:
- v_0 is the initial velocity of the bomb (100 m/s)
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
- t is the time taken for the bomb to reach the ground (30 seconds)
Plugging in the values, we have:
h = (100 * 30) - (0.5 * 9.8 * (30^2))
h = 3000 - 4410
h = -1410 meters
In this case, the negative value means that the balloon is below the starting point.
Therefore, when the balloon is ascending with a speed of 100 m/s when the bomb is dropped, the height of the balloon is -1410 meters relative to its starting position.