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
I need the answer to this quest please!!!!!
812:12km
I need the answer to this question please!!!!!!!!!!!!!!
The problem that made me not to solve ahead is the west wind which is 70km/hr^-1
To find the distance of the plane from its base in 2 hours, we can use the concept of vector addition.
Given:
Velocity of the plane = 400 km/hr (north)
Velocity of the wind = 70 km/hr (west)
We need to find the resultant velocity of the plane, which will give us the direction and magnitude of its movement.
Step 1: Resolve the velocities into their respective components.
The velocity of the plane can be resolved into north and west components. Since the plane is moving only north, the north component will be the full magnitude of the velocity, which is 400 km/hr. The west component will be zero since the plane is not moving westward.
The velocity of the wind is blowing westward, so the west component is 70 km/hr, and the north component is zero.
Step 2: Add the components to get the resultant velocity.
To find the resultant velocity, we add the respective components of the plane and the wind.
The resultant velocity in the north direction is:
400 km/hr + 0 km/hr = 400 km/hr (north)
The resultant velocity in the west direction is:
0 km/hr + (-70 km/hr) = -70 km/hr (west)
Step 3: Calculate the distance using the resultant velocity.
To find the distance, we can use the formula:
Distance = Speed * Time
Distance = Resultant velocity * Time
Distance = √[(resultant north velocity)^2 + (resultant west velocity)^2] * Time
Substituting the values:
Distance = √[(400 km/hr)^2 + (-70 km/hr)^2] * 2 hrs
Calculating further:
Distance = √[160000 km^2/hr^2 + 4900 km^2/hr^2] * 2 hrs
Distance = √[164900 km^2/hr^2] * 2 hrs
Distance ≈ √164900 km * 2 hrs
Distance ≈ 406.12 km * 2 hrs
Distance ≈ 812.24 km
Therefore, the distance of the plane from its base in 2 hours is approximately 812.24 km.