Step 1: Calculate the vertical altitude ($y$)
The maximum angle of elevation occurs at $t = 50 \text{ min}$. Since the ascent velocity is constant at $v_y = 8 \text{ m/min}$: $$ y = v_y \times t $$ $$ y = 8 \times 50 = 400 \text{ m} $$

Step 2: Calculate total horizontal distance ($x_{total}$)
At this instant, the angle of elevation is $53^\circ$. Considering the right-angled triangle formed by the telescope and the balloon: $$ \tan(53^\circ) = \frac{y}{x_{total}} $$ $$ \frac{4}{3} = \frac{400}{x_{total}} $$ $$ x_{total} = \frac{400 \times 3}{4} = 300 \text{ m} $$

Step 3: Calculate Horizontal Drift
The balloon started at a horizontal distance $l = 100 \text{ m}$ from the telescope. The wind caused it to drift horizontally to a final distance of $x_{total} = 300 \text{ m}$. $$ \text{Drift} = x_{total} – l $$ $$ \text{Drift} = 300 \text{ m} – 100 \text{ m} $$ $$ \text{Drift} = 200 \text{ m} $$