Question

Two velocities, 10 m/s and 15 m/s, are inclined at an angle of 60 degrees to each other. Obtain the resultant velocity by graphical and analytical methods.

a) 12 m/s
b) 14 m/s
c) 16 m/s
d) 18 m/s

Answer 1

By using the law of cosines with the given velocities and angle, the resultant velocity can be calculated to be approximately 13.2 m/s, which makes 14 m/s (option b) the closest answer provided. Option B is correct.

Step-by-step explanation:

The student asked about obtaining the resultant velocity when two velocities, 10 m/s and 15 m/s, are inclined at an angle of 60 degrees to each other. To find the resultant velocity analytically, we can use the law of cosines:

v2 = v12 + v22 - 2 * v1 * v2 * cos(θ)

v1 = 10 m/s

v2 = 15 m/s

θ = 60 degrees

Plugging in the values:

v2 = 102 + 152 - 2 * 10 * 15 * cos(60°)

v2 = 100 + 225 - 300 * 0.5

v2 = 325 - 150

v2 = 175

v = √175

v ≈ 13.2 m/s

Thus, the correct answer by analytical methods is not listed among the options provided. When selecting from the given options, 14 m/s (option b) is the closest to the accurate result.