Question

Two vectors, of magnitudes 20 and 50, are added. Which one of the following is a possible answer for the magnitude of the resultant?

a. 10
b. 20
c. 40
d. 80.

Answer 1

Answer:(c) 40

Explanation:

Given

Magnitude of first vector is 20 units

Magnitude of second vector is 50 units

From the given data we can say that maximum magnitude of resultant vector is 70 units if the angle between is
`0^(\circ)`

and the minimum value of resultant is 50-20=30 if they are
`180^(\circ)` apart

So the resultant must lie between 30 to 70

Thus c is the only option which satisfy the above deductions.

Answer 2

(c) 40

Explanation:

Let the resultant of the two vector is R

So
`R=√(20^2+20^2+2* 20* 50* cos\Theta )`

Squaring both side
`R^2=2900+2000cos\Theta`

`cos\Theta =(R^2-2900)/(2000)`

We know that
`-1\leq cos\Theta \geq 1`

So
`-1\leq (R^2-2900)/(2000) \geq 1`

Taking right part
`R^2\leq 4900`

`R\leq 70`

Now taking left part
`-2000\leq R^2 -2900`

`R\geq 30`

So the value of resultant should be in between 30 and 70

Which is 40 in the option so option c is correct option