A bird is flying at a speed of 15 km/h due East. It then makes a sudden turn to the North, but continues to travel at a speed of 15 km/h. Which changed, speed or velocity, both, or neither? Explain your reasoning.

Velocity is a vector quantity that is easily affected by changes in the direction of motion.
The presence of this displacement vector causes the resultant velocity to be 15√2 m/s.

Explanation

Hi ! Here I will discuss about velocity and speed. velocity is different from speed. Velocity depends on displacement (movement relative to the starting point) divided by the value of time. On the other hand, speed depends only on distance (how far the object is moving) regardless of the starting point of the movement. Therefore, velocity is called a vector quantity (a value that is easily influenced by direction), while speed is called a scalar quantity because it does not care about direction.

Proof

Why do I say there that the resultant velocity is 15√2 m/s ? This is because there is a double direction that makes it necessary to calculate the resultant using the formula:

[tex] \sf{\sum v = \sqrt{(v_1)^2 + (v_2)^2 + 2(v_1)(v_2) \cos(\theta)}} [/tex] >> [tex] \sf{\theta} [/tex] = 90°

[tex] \sf{\sum v = \sqrt{(15)^2 + (15)^2 + 2(15)(15) \cos(90^o)}} [/tex]

[tex] \sf{\sum v = \sqrt{225 + 225 + 2(15)(15) (0)}} [/tex]

[tex] \sf{\sum v = \sqrt{450 + 0}} [/tex]

[tex] \sf{\sum v = \sqrt{225 \times 2}} [/tex]

[tex] \sf{\sum v = 15 \sqrt{2} \: m/s} [/tex] (Q.E.D)