a plane flying due north at 100 m/s is blown by
a. 50 m/s strong wind due east.
b. what is the plane's resultant velocity?
A plane flying due north at 100 m/s is blown by a strong wind at 500 m/s due east. What is the magnitude of the plane’s resultant velocity?
How much energy is required to increase the speed of a car from 10 m/s to 25 m/s if its mass is 1500 kg?
A plane flying due north at 100s/m-1is blown due west at 50m/s-1by a strong wind. Find the resultant velocity of the plane.
To find the resultant velocity of the plane, we can use vector addition.
First, let's represent the velocity of the plane as a vector pointing due north at 100 m/s. We'll call this vector V1.
Next, we'll represent the velocity of the wind as a vector pointing due east at 50 m/s. We'll call this vector V2.
To find the resultant velocity, we need to add these two vectors. Since they are perpendicular to each other (one pointing north, the other east), we can use the Pythagorean theorem and trigonometry.
- Step 1: Calculate the magnitude of the resultant velocity using the Pythagorean theorem.
The magnitude of the resultant velocity can be calculated as:
Resultant Velocity (magnitude) = sqrt((V1)^2 + (V2)^2)
In this case, V1 is 100 m/s and V2 is 50 m/s.
Magnitude = sqrt((100)^2 + (50)^2) = sqrt(10000 + 2500) = sqrt(12500) = 111.8 m/s (rounded to one decimal place).
- Step 2: Calculate the direction of the resultant velocity.
Since the wind is blowing due east and the plane is flying due north, the vectors form a right triangle.
The angle between the resultant velocity and the north direction can be found using trigonometry.
We can use the inverse tangent function (arctan) to calculate this angle.
Angle = arctan(V2 / V1) = arctan(50 / 100) = arctan(0.5) = 26.6 degrees (rounded to one decimal place).
So, the resultant velocity of the plane is approximately 111.8 m/s in a direction 26.6 degrees east of north.
100^2 + 50^2 = v^2
Θ is the angle East of North
tan(Θ) = 50 / 100 = .5