Question

Plane A is flying at 440 mph in the northeast direction relative to the Earth. Plane B is flying at 550 mph in the north direction relative to the Earth. What is the speed of Plane B as observed from Plane A?a. 532 mphb. 860 mphc. 362 mphd. 659 mphe. 669 mph

Answer 1

Answer:

The speed of plane B relative to plane A is 392.25 mph.

Step-by-step explanation:

Speed of plane A = 440 mph north east

speed of plane B = 550 mph north

speed of plane A = $440(cos 45 \widehat{i} + sin 45 \widehat{j})=311.1 \widehat{i} + 311.1 \widehat{j}$

speed of plane B = $550 \widehat{j}$

Speed  of plane B with respect to plane A is

= speed of plane B - speed of plane A

$=550 \widehat{j} - 311.1 \widehat{i} - 311.1 \widehat{j}\\\\=-311.1 \widehat{i} + 238.9 \widehat{j}\\\\= \sqrt{311.1^2 + 238.9^2 }\\\\=392.25 mph$