Acoin is dropped from a hot-air balloon that is 300 m above the ground and rising at 10.0 m/s upward. for the coin, find (a) the maximum height reached, (b) its position and velocity 4.00 s after being released, and (c) the time before it hits the ground

a) Maximum height will be .

b) .

c) The time before it hits the ground is .

Explanation:

Initial position:

Initial velocity:

Gravity's acceleration:

a) From Kinematics:

⇒

When the coin reaches it's maximum height, it's velocity will be

⇒ ⇒ .

Maximum height will be .

b) From Kinematics, the movement law will be:

where is the position where the coin is dropped.

At :

.

c) Again, we have that:

Now, if final is , then

.

We need to use the resolvent to solve this equation:

⇒ .