A transport drone P of length 540 meters passes over a landing deck in 22 seconds and flies past a stationary signal tower in 18 seconds. The ratio of the speed of drone P to drone Q is 5 : 2, and drone Q passes a vertical indicator pole in 20 seconds. Find the length of the landing deck as a percentage of the length of drone Q.

Correct Answer: 50%

Step-by-Step Explanation:

Step 1: Calculate the speed of drone P

When drone P passes a stationary signal tower, the distance traveled by the drone is equal to its own length.

Length of drone P = 540 meters

Time taken to pass the signal tower = 18 seconds

Using the formula for speed:

$\text{Speed of drone P}=\frac{\text{Length of drone P}}{\text{Time taken}}$

$\text{Speed of drone P}=\frac{540}{18}=30\text{meters/second}$

Step 2: Find the length of the landing deck

When drone P passes over the landing deck, the total distance covered is equal to the length of drone P plus the length of the landing deck.

Time taken to pass the landing deck = 22 seconds

Total distance covered = Speed of drone P × Time taken

$\text{Total distance}=30\times 22=660\text{meters}$

Since Total distance = Length of drone P + Length of landing deck:

$660=540+\text{Length of landing deck}$

$\text{Length of landing deck}=660-540=120\text{meters}$

Step 3: Calculate the speed and length of drone Q

We are given that the ratio of the speed of drone P to drone Q is 5 : 2.

$\frac{\text{Speed of P}}{\text{Speed of Q}}=\frac{5}{2}$

$\text{Speed of Q}=30\times \frac{2}{5}=12\text{meters/second}$

Drone Q passes a vertical indicator pole in 20 seconds. The distance covered in this time is equal to the length of drone Q.

$\text{Length of drone Q}=\text{Speed of Q}\times \text{Time taken}$

$\text{Length of drone Q}=12\times 20=240\text{meters}$

Step 4: Calculate the required percentage

We need to find the length of the landing deck as a percentage of the length of drone Q:

$\text{Percentage}=\left(\frac{\text{Length of landing deck}}{\text{Length of drone Q}}\right)\times 100$

$\text{Percentage}=\left(\frac{120}{240}\right)\times 100=50\%$

Therefore, the length of the landing deck is 50% of the length of drone Q.