A hot-air balloon is rising upward with a constant speed of 2.21 m/s. When the balloon is 2.25 m above the ground, the balloonist accidentally drops a compass over the side of the balloon. How much time elapses before the compass hits the ground?
98986
2.34
To find the time it takes for the compass to hit the ground, we can use the equation of motion:
s = ut + (1/2)at^2
Where:
- s is the distance the compass travels (2.25 m),
- u is the initial velocity (in this case, the upward velocity of the hot-air balloon, which is 2.21 m/s),
- t is the time it takes for the compass to hit the ground, and
- a is the acceleration (which is equal to the acceleration due to gravity, approximately 9.8 m/s^2).
Since the compass is dropped from rest (its initial velocity is 0), the equation simplifies to:
s = (1/2)at^2
Rearranging the equation to solve for time, we have:
t^2 = 2s/a
t = sqrt(2s/a)
Substituting the given values, we get:
t = sqrt((2 * 2.25 m) / 9.8 m/s^2)
t ā 0.478 s
Therefore, it takes approximately 0.478 seconds for the compass to hit the ground.