Two air crafts p and q are flying at the same speed 300 m/s .the direction along which p is flying is at right angle to the direction along which q is flying then find the magnitide of velocity of p relative to q
say
Q = 300 i + 0 j
P = 0 i +300 j
then
P-Q= -300i + 300 j
|P-Q| = magnitude of relative velocity = 300 sqrt 2
tan angle = -1
angle = 45 degrees (P falling behind Q in x)
Pq=√Vp^+Vq^. Pq=√300^+300^=424.3
To find the magnitude of the velocity of P relative to Q, we can use the Pythagorean theorem.
Since aircraft P is flying at a right angle to the direction of aircraft Q, their velocities can be treated as perpendicular components of a right triangle.
Let's assume that the velocity of aircraft P is represented by vector P, and the velocity of aircraft Q is represented by vector Q.
The magnitude of the velocity of P relative to Q can be found by calculating the magnitude of the vector resulting from subtracting vector Q from vector P.
The magnitude of the velocity of P relative to Q (VPQ) can be calculated as follows:
VPQ = sqrt((VP)^2 + (VQ)^2)
Given that both aircraft P and Q are flying at the same speed of 300 m/s, the magnitude of the velocity of P and Q (assuming VP = VQ = 300 m/s) can be substituted into the formula:
VPQ = sqrt((300 m/s)^2 + (300 m/s)^2)
VPQ = sqrt(90000 m^2/s^2 + 90000 m^2/s^2)
VPQ = sqrt(180000 m^2/s^2)
VPQ ≈ 424.26 m/s (rounded to two decimal places)
Therefore, the magnitude of the velocity of P relative to Q is approximately 424.26 m/s.
To find the magnitude of the velocity of p relative to q, we need to consider the vector sum of their velocities.
Since the directions along which p and q are flying are at right angles to each other, we can use Pythagoras' theorem to find the magnitude of the velocity of p relative to q.
Let's label the magnitude of the velocity of p relative to q as v_pq. Using Pythagoras' theorem:
v_pq = √((v_p)^2 + (v_q)^2)
Where v_p is the velocity of p and v_q is the velocity of q.
Given that both p and q are flying at the same speed of 300 m/s, we can substitute their values into the equation:
v_pq = √((300)^2 + (300)^2)
= √(90000 + 90000)
= √(180000)
= 424.26 m/s (rounded to two decimal places)
Therefore, the magnitude of the velocity of p relative to q is approximately 424.26 m/s.