Final answer:
After 4.00 seconds, the coin will be approximately 78.4 meters below the starting position. The maximum height reached by the coin is approximately 5.10 meters.
Step-by-step explanation:
The hot-air balloon is rising at a velocity of 10.0 m/s upward. When the coin is dropped from the balloon, it will also have an initial velocity of 10.0 m/s. Using the equations of motion, we can find the maximum height reached by the coin:
(a) Maximum height reached:
We can use the equation:
vf^2 = vi^2 + 2ad
0 = 10^2 + 2(-9.8)d
-100 = -19.6d
d = 100/19.6
d ≈ 5.10 meters
Therefore, the maximum height reached by the coin is approximately 5.10 meters.
(b) Position and velocity after 4.00 s:
After 4.00 seconds, the coin will continue to fall downward with an acceleration of -9.8 m/s^2. We can find the position and velocity using the equations of motion:
d = vit + (1/2)at^2
d = (0)(4) + (1/2)(-9.8)(4^2)
d = -78.4 meters
Therefore, after 4.00 seconds, the coin will be approximately 78.4 meters below the starting position.
(c) Time before hitting the ground:
We can use the equation:
d = vit + (1/2)at^2
300 = 10t + (1/2)(-9.8)t^2
0 = 4.9t^2 + 10t - 300
Using the quadratic formula, we find:
t = (-b ± √(b^2 - 4ac))/(2a)
t = (-10 ± √(10^2 - 4(4.9)(-300)))/(2(4.9))
t ≈ 15.5 seconds
Therefore, the time taken for the coin to hit the ground is approximately 15.5 seconds.