2 velocities each 5m/so are inclined at 60 degree .find their resultant
Since the two vectors are equal, the parallelogram of vectors is a rhombus, and the length of diagonal becomes two times the component of each on the bisector, namely
R=5m/s*cos(30°)
along the bisector of the 60° angle.
In other words, if we resolve the two vectors along the bisector, the components along the bisector add up, while the components perpendicular to it cancels.
To find the resultant of two velocities inclined at an angle, we can use the vector sum.
Let's denote the magnitude of the first velocity as V1 = 5 m/s.
Now, let's find the horizontal and vertical components of the first velocity:
Horizontal component of V1 = V1 * cos(60°)
Vertical component of V1 = V1 * sin(60°)
Substituting the values, we get:
Horizontal component of V1 = 5 * cos(60°) = 5 * 0.5 = 2.5 m/s
Vertical component of V1 = 5 * sin(60°) = 5 * (√3/2) = 8.66 m/s
Similarly, let's denote the magnitude of the second velocity as V2 = 5 m/s.
The horizontal and vertical components of the second velocity will be the same since they have the same magnitude.
Horizontal component of V2 = V2 * cos(60°) = 5 * 0.5 = 2.5 m/s
Vertical component of V2 = V2 * sin(60°) = 5 * (√3/2) = 8.66 m/s
Next, we add the horizontal and vertical components of the velocities to find the resultant:
Horizontal component of the resultant = Sum of horizontal components = 2.5 m/s + 2.5 m/s = 5 m/s
Vertical component of the resultant = Sum of vertical components = 8.66 m/s + 8.66 m/s = 17.32 m/s
Finally, we can find the magnitude of the resultant velocity (resultant speed) using the Pythagorean theorem:
Resultant speed = √((Horizontal component of the resultant)^2 + (Vertical component of the resultant)^2)
Resultant speed = √((5 m/s)^2 + (17.32 m/s)^2) = √(25 m^2/s^2 + 299.46 m^2/s^2) = √324.46 m^2/s^2 = 18 m/s
Therefore, the magnitude of the resultant velocity is 18 m/s.
To find the resultant velocity of the two given velocities, we can use the parallelogram law of vector addition. This law states that if two vectors are represented by the adjacent sides of a parallelogram, then the diagonal passing through their common point represents the resultant vector.
Here are the steps to find the resultant velocity:
Step 1: Draw a rough diagram illustrating the two given velocities. Place one vector horizontally and represent it as V1. Then draw the second vector inclined at an angle of 60 degrees upward and represent it as V2. Ensure that the tip of V1 and the tail of V2 meet at a common point.
Step 2: From the common point, draw the diagonal of the parallelogram that connects the tail of V1 to the tip of V2. This diagonal represents the resultant vector, denoted as VR.
Step 3: To find the magnitude of VR, we can use the law of cosines. The equation for finding the magnitude is given by:
VR^2 = V1^2 + V2^2 - 2 * V1 * V2 * cos(theta)
In this equation, V1 and V2 are the magnitudes of the given velocities (both equal to 5 m/s), and theta is the angle between them (60 degrees).
VR^2 = 5^2 + 5^2 - 2 * 5 * 5 * cos(60 degrees)
VR^2 = 25 + 25 - 2 * 5 * 5 * 0.5
VR^2 = 50 - 25 = 25
VR = sqrt(25) = 5 m/s
Step 4: Determine the direction of VR. In this case, since V2 is inclined at 60 degrees upward from the horizontal axis, the resultant vector VR will also be inclined at an angle of 60 degrees upward from the horizontal axis.
Therefore, the resultant velocity is 5 m/s at an angle of 60 degrees upward from the horizontal axis.
Note: The units in this example are meters per second (m/s), but make sure to use consistent units when solving problems.