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Three points are located at the vertices...

Three points are located at the vertices of an equilateral triangle each of whose sides measure a. They all start simultaneously with speed v, each aiming at the next in order. How soon will the points converge ?

Text Solution

Verified by Experts

The correct Answer is:
B
The mutual velocity of approach `=v-(-v cos 60^(@))=(3v)/2` The initial relative separation `a` is reduced to zero at this rate `a=int_(2)^(3v)dtrArra=(3v)/2t`
`rArr t= (2a)/(3v)=(2xx3)/(3xx1)=2s`
The points will meet at the incentre of the triangle.
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Knowledge Check

  • Find the area of equilateral triangle whose each side is 20 cm.

    A
    `(100)/(sqrt(3)) cm^2`
    B
    `100 sqrt(3) cm^2`
    C
    `100 (sqrt(3))/(2) cm^2`
    D
    `100 (sqrt(3))/(4)

  • Each side of an equilateral triangle measures 8 cm. The area of the triangle is

    A
    `8 sqrt(3) cm^(2)`
    B
    `sqrt(3/4) xx 8^2 cm^(2)`
    C
    `32 sqrt(3) cm^(2)`
    D
    48 `cm^(2)`

  • Find the area of an isosceles triangle each of whose equal sides measures 13 cm and whose base measures 20 cm.

    A
    53.06 `cm^(2)`
    B
    63.06 `cm^(2)`
    C
    83.06 `cm^(2)`
    D
    73.06 `cm^(2)`