### A coin 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.

**Solution:**

**PART A**

For the coin, we are given the following:

The maximum height reached can be solved using the formula

Solve for Δy in terms of the other variables

Now, substitute the given values

From the moment the coin is dropped to the top of the ascent, the change in position of the coin is +5.10 m. Therefore, the maximum height is

**PART B**

The position of the coin after 4 seconds can be solved using the formula

Substitute the given values

The change in position of the coin is -38.4 m. Therefore, the poisiton of the coin with respect to the ground is

The velocity after 4 seconds is given by the formula

Substitute the given values

The velocity is 29.2 m/s, downward.

**PART C**

The time it takes for the coin to hit the ground can be solved using the formula

Substitute the given values

Simplify and rearrange the equation to form a quadratic equation

Now, we can solve for time, t, using the quadratic formula

The time of flight is 8.91 seconds.