Question

. During training, an athlete sprints 30 m East and then 40 m West.
Identify the row in the table which gives the distance travelled and the displacement from the
starting point.

Answer 1

Answer:

Step-by-step explanation:

if two vectors acting simultaneously at a point can be represented both in magnitude and direction by the adjacent sides of a parallelogram drawn from a point, then the resultant vector is represented both in magnitude and direction by the diagonal of the parallelogram passing through that point.

derivation of the law

let p and q  be two vectors acting simultaneously at a point and represented both in magnitude and direction by two adjacent sides oa and od of a parallelogram oabd as shown in figure.

let  θ be the angle between  p  and  q  and  r  be the resultant vector.  then, according to parallelogram  law of vector addition, diagonal  ob represents the resultant of  p  and  q.

so, we have

                   r  =  p  +  q

now, expand a to c and draw bc perpendicular to  oc.

from triangle ocb,

       

in triangle abc,

       

also,

       

magnitude of resultant:

substituting value of ac and bc in (i), we get

       

is the magnitude of resultant.

direction of resultant:   let  ø be the angle made by  resultant  r  with  p. then,

from triangle obc,

       

is the direction of resultant.