Question 19

Explanation

Plane Movement Visualization

Given:

• Plane altitude $h = 3000 \text{ m}$.
• Initial elevation angle $\alpha = 30^\circ$.
• Final elevation angle $\beta = 45^\circ$.
• Time elapsed $t = 30 \text{ seconds}$.

Calculate Initial Horizontal Distance

The initial horizontal distance ($x_1$) can be calculated using the tangent of $30^\circ$:

Calculate Final Horizontal Distance

The final horizontal distance ($x_2$) can be calculated using the tangent of $45^\circ$:

Calculate Horizontal Distance Traveled

The horizontal displacement ($\Delta x$) is the difference between the initial and final distances:

Calculate Speed

Speed ($v$) is distance divided by time:

Thus, the estimated speed of the plane is $100(\sqrt{3} - 1) \text{ m/s}$.