A hot-air balloon is rising upward with a constant speed of 3.93 m/s. When the balloon is 4.91 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 = -3.93t * 4.9t^2 = 4.91 m.
4.9t^2 - 3.93t - 4.91 = 0
Use Quadratic Formula and get:
t = 1.48 s.
To find the time it takes for the compass to hit the ground, we need to calculate the time it takes for the compass to drop from a height of 4.91 m.
We can use the kinematic equation for vertical motion:
Δy = v₀t + (1/2)gt²
where:
Δy = change in height (4.91 m)
v₀ = initial velocity (0 m/s since the compass is dropped)
t = time
g = acceleration due to gravity (approximately 9.8 m/s²)
Rearranging the formula, we get:
t = √(2Δy / g)
Now, we can substitute the given values:
t = √(2 * 4.91 m / 9.8 m/s²)
t = √(0.999 m / 9.8 m/s²)
t ≈ 0.45 seconds
Therefore, it takes approximately 0.45 seconds for the compass to hit the ground.