A pilot takes off at a point A and ascends at a fixed angle with the level runway if he flies a distamce of 2500 yards but covers only a ground distance of 2200 yards then what is his amgle of ascent?

Answer 1

To find the angle of ascent, we can use the sine function in a right triangle, where the vertical distance (altitude) is the opposite side, the ground distance is the adjacent side, and the angle of ascent is what we're solving for. The relationship can be expressed as ( \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} ). In this case, the hypotenuse is 2500 yards and the ground distance (adjacent) is 2200 yards.

Using the Pythagorean theorem, we first find the vertical distance (altitude):

[ \text{altitude} = \sqrt{(2500)^2 - (2200)^2} \approx 1200 \text{ yards} ]

Then, we calculate the angle:

[ \sin(\theta) = \frac{1200}{2500} \Rightarrow \theta \approx \arcsin(0.48) \approx 28.5^\circ ]

Thus, the angle of ascent is approximately 28.5 degrees.