Question

1. A drone is launched with a velocity of 51 m/s, 67. Three minutes after the drone is launched it suddenly changed its course to 30 m/s, 226 to avoid high trees on its way. Then, it finally goes back at a rate of 31 m/s, 52. Calculate for the total resultant vector of the drone.

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Criteria:

Table of components

Illustration, Given & Required​

​​Equation and Solution

​ ​Final Answer   

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Answer 1

vector a = 51 m/s, 67 m/s is shown in red.

vector b = 30 m/s, 226 m/s is shown in blue.

vector c = 31 m/s, 52 m/s is shown in green.

The resultant vector is shown in grey colour in the graph.

Polygon law:

The polygon law is an extension of earlier two laws of vector addition. It is successive application of triangle law to more than two vectors. A pair of vectors (a, b) is added in accordance with triangle law. The intermediate resultant vector (a + b) is then added to third vector (c) again, successively till all vectors to be added have been exhausted.

Let the resultant vector be R.

R = a + b + c

= (51 cos 67 i + 51 sin 67 j ) + (30 cos 226 i + 30 sin 226 j ) + (31 cos 52 i + 31 sin 52 j )

= 18.173 i + 49.7938 j m/s

Magnitude of R = ((18.173)² + (49.7938)²)^1/2 m/s = 53.0064 m/s

Angle = tan^-1(49.7938 / 18.173) = 69.9497

Answer : Total resultant vector of the drone is 53.0064 m/s , 69.9497.