Step 1: Understanding the Concept:
When released, the stone inherits the velocity of the balloon.
It will first travel upward, momentarily come to rest at its peak, and then fall back down to the ground. Step 2: Key Formula or Approach:
Maximum height reached from release point is $h = \frac{u^2}{2g}$.
Total distance = (Upward distance to peak) + (Downward distance back to release level) + (Distance to the ground). Step 3: Detailed Explanation:
Initial velocity of stone $u = 10 \text{ m/s}$ (upward).
Release height $H = 75 \text{ m}$.
Acceleration $a = -g = -10 \text{ m/s}^2$.
The upward distance traveled before velocity becomes zero:
\[ h = \frac{u^2}{2g} = \frac{10^2}{2 \times 10} = \frac{100}{20} = 5 \text{ m} \]
The stone goes 5 m up, then falls 5 m back to the release height, and finally falls 75 m to the ground.
Total distance $D = 5 \text{ (up)} + 5 \text{ (down to 75m mark)} + 75 \text{ (to ground)}$.
\[ D = 5 + 5 + 75 = 85 \text{ m} \] Step 4: Final Answer:
The distance travelled by the stone is 85 m.
