A student is standing in the basket of a hot air-ballon which is moving upwards at a constant speed of 15 m.s.-1.He leans over the edge of the basket and lets go of the sandbag which takes 5 seconds to reach the ground.what is the acceleration of the hot-air balloon while the sandbag is in it?
To find the acceleration of the hot air balloon while the sandbag is in it, we can use the kinematic equation:
d = (1/2) * a * t^2
where:
d is the distance traveled by the sandbag (which is equal to the height of the hot air balloon from the ground),
a is the acceleration of the hot air balloon, and
t is the time it takes for the sandbag to reach the ground.
First, let's calculate the distance traveled by the sandbag:
d = 0.5 * g * t^2
where:
g is the acceleration due to gravity, which is approximately 9.8 m/s^2 on Earth.
Given that t = 5 seconds, we can calculate the distance:
d = 0.5 * 9.8 * 5^2
d = 0.5 * 9.8 * 25
d ≈ 120.25 meters (rounded to two decimal places)
Since the hot air balloon is moving upwards at a constant speed of 15 m/s, the distance traveled by the hot air balloon is equal to the distance traveled by the sandbag. Therefore, the height of the hot air balloon from the ground is also approximately 120.25 meters.
Now, we can use the kinematic equation to find the acceleration (a) of the hot air balloon:
120.25 = 0.5 * a * 5^2
240.5 = 25a
a = 240.5 / 25
a ≈ 9.62 m/s^2 (rounded to two decimal places)
Therefore, the acceleration of the hot air balloon, while the sandbag is in it, is approximately 9.62 m/s^2.