A hot-air balloon is rising upward with a constant speed of 2.65 m/s. When the balloon is 3.40 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?
h = Vo*t + 0.5g*t^2.
h = 3.40 m/s.
Vo = -2.65 m/s.
g = +9.8 m/s^2.
t = ?.
Henry you didn't answer the question
To find the time it takes for the compass to hit the ground, we can use the equation of motion for objects in free fall.
First, let's consider the vertical motion of the compass. Since the balloon is rising upward with a constant speed, the initial velocity of the compass is 0 m/s. The acceleration due to gravity is approximately 9.8 m/s², directed downward (negative direction). The distance the compass falls is the height of the balloon above the ground, which is 3.40 m.
We can use the equation:
h = (1/2) * g * t²
where h is the distance, g is the acceleration due to gravity, and t is the time.
Rearranging the equation, we get:
t² = (2 * h) / g
Substituting the values for h and g, we have:
t² = (2 * 3.40) / 9.8
Simplifying the equation gives:
t² = 0.6939
Taking the square root of both sides, we find:
t ≈ 0.834 s
So, approximately 0.834 seconds will elapse before the compass hits the ground.