Two aircraft p and q are flying at the same speed,300m/s-1 the direction along which p is flying is at right angle to the direction along to which q is flying, find the magnitude of the velocity the aircraft p relative to aircraft q ?
To find the magnitude of the velocity of aircraft P relative to aircraft Q, we can use vector addition. Since the two aircraft are flying at right angles to each other and at the same speed, we can use the Pythagorean theorem.
Let's consider the velocity of aircraft P as Vp and the velocity of aircraft Q as Vq.
Since Vp and Vq are perpendicular to each other, we can represent the velocity of P relative to Q as the hypotenuse of a right-angled triangle, with Vp as one side and Vq as the other side.
Using the Pythagorean theorem, we can calculate the magnitude of the velocity of aircraft P relative to aircraft Q:
Magnitude of Vp relative to Q = √(Vp^2 + Vq^2)
Given that the speed of both aircraft is 300 m/s^2, we substitute the values into the equation:
Magnitude of Vp relative to Q = √(300^2 + 300^2)
Simplifying further:
Magnitude of Vp relative to Q = √(2 * 300^2)
Magnitude of Vp relative to Q = √(90000)
Magnitude of Vp relative to Q ≈ 300 m/s
Therefore, the magnitude of the velocity of aircraft P relative to aircraft Q is approximately 300 m/s.