an airplane normally flies at 200 km/h, what is the resultant velocity of the plane if it experiences a 50 km/h tail wind, and a 50km/h head wind
To calculate the resultant velocity of the airplane, we need to consider the effect of both the tailwind and the headwind.
First, we need to understand the concept of relative velocities. When an object moves in a fluid medium, such as air, its motion is relative to that medium. When there is a tailwind, the airplane's motion is greater than its normal speed, and when there is a headwind, its motion is slower than its normal speed.
In this case, the airplane's normal speed is 200 km/h. When it experiences a 50 km/h tailwind, the airplane's speed is effectively increased by 50 km/h. Therefore, the speed of the airplane with a tailwind is 200 km/h + 50 km/h = 250 km/h.
On the other hand, when the airplane experiences a 50 km/h headwind, the airplane's speed is effectively decreased by 50 km/h. Therefore, the speed of the airplane with a headwind is 200 km/h - 50 km/h = 150 km/h.
Now, to find the resultant velocity of the airplane, we need to consider the vector sum of the tailwind and headwind velocities. Since the tailwind and headwind are in opposite directions, we subtract the headwind velocity from the tailwind velocity.
Resultant Velocity = Tailwind Velocity - Headwind Velocity
= 250 km/h - 150 km/h
= 100 km/h
Therefore, the resultant velocity of the plane is 100 km/h.