a plane is headed north with a velocity of 400km/hr and west wind blowing at 70km/hr.find the distance of the plane from its base in 2hrs
To find the distance of the plane from its base in 2 hours, we can break down the problem into components and use the Pythagorean theorem.
Let's define the north direction as the positive y-direction, and the west direction as the negative x-direction.
The plane's velocity towards the north is 400 km/hr, but we need to convert the velocity to distance for 2 hours. To find the distance, we can multiply the velocity by the time:
Distance north = Velocity north × Time
Distance north = 400 km/hr × 2 hr = 800 km
Next, we need to consider the effect of the wind blowing west at 70 km/hr. This wind will act against the plane's motion, reducing the effective velocity towards the west.
The total velocity towards the west is the combination of the plane's westward velocity and the wind's eastward velocity. Since the wind is blowing in the west direction (a negative x-direction), we subtract the wind velocity from the plane's velocity:
Velocity west = Plane's velocity west - Wind's velocity east
Velocity west = 0 km/hr - 70 km/hr = -70 km/hr
Again, we convert this velocity to distance for 2 hours:
Distance west = Velocity west × Time
Distance west = -70 km/hr × 2 hr = -140 km
Now, we can use these distances to find the total distance of the plane from its base using the Pythagorean theorem.
Total distance = √(Distance north^2 + Distance west^2)
Total distance = √(800^2 + (-140)^2)
Total distance ≈ √(640,000 + 19,600)
Total distance ≈ √659,600
Total distance ≈ 812.03 km
Therefore, the distance of the plane from its base after 2 hours is approximately 812.03 km.