Kinematics

Let the balloon be rising with a uniform velocity ft/sec. When the stone is let go, it has an initial velocity equal to the velocity of the balloon, which is ft/sec upwards.

Step 1: Motion of the stone after it is dropped
The stone is subjected to gravity with acceleration ft/sec² downwards. The position of the stone after time is given by the equation: where is the height of the stone above the ground at time , and is the initial upward velocity of the stone (which is equal to the velocity of the balloon when it is released).

Step 2: Find the height of the stone when it hits the ground
The stone reaches the ground when its height . Substituting ft/sec² and sec (since the stone reaches the ground after 4 seconds): Simplifying:

Step 3: Height of the balloon when the stone hits the ground
The height of the balloon at seconds is given by: So, the height of the balloon when the stone reaches the ground is 240 feet.

Step 4: Height of the balloon when the stone is released
Since the stone was released from the balloon at a height of ft, the height of the balloon when the stone reaches the ground is:

Answer: