An airplane traveled 300 km northeast in 2 hours. Find the velocity of the plane.
watch the units:
300km/2hr = 300/2 km/hr
an airplane traveled 300 km northeast in 2.5 hours. find the speed of the plane.
To find the velocity of the plane, we need to know both the displacement (change in position) and the time taken.
In this case, we are given that the plane traveled 300 km northeast in 2 hours. The direction of northeast can be represented by a 45-degree angle with respect to the positive x-axis.
First, we can calculate the displacement of the plane using the given information. Since the plane traveled northeast, we can break down the displacement into its x and y components.
The x-component of displacement = distance * cosine(angle)
The y-component of displacement = distance * sine(angle)
Using the given distance of 300 km and the angle of 45 degrees, we can calculate the x-component and y-component of displacement:
x-component = 300 km * cos(45°) = 300 km * 0.7071 = 212.1 km
y-component = 300 km * sin(45°) = 300 km * 0.7071 = 212.1 km
Now, we have the displacement in both the x and y directions. To find the total displacement vector, we can use the Pythagorean theorem:
Total displacement = √(x-component^2 + y-component^2)
= √(212.1 km)^2 + (212.1 km)^2)
= √(44944.41 km^2 + 44944.41 km^2)
= √(89888.82 km^2)
≈ 299.8 km
So, the magnitude of the displacement, which represents the total distance traveled by the plane, is approximately 299.8 km.
To find the velocity, we use the formula:
Velocity = Displacement / Time
In this case, the displacement is 299.8 km and the time is 2 hours:
Velocity = 299.8 km / 2 hours
= 149.9 km/h
Therefore, the velocity of the plane is 149.9 km/h approximately.