Question

A bag of mass m hangs by a ling thread. A bullet of mass m comes horizintally

Answer 1

Step 1 :

The vertex is the lowest point of the cable.

Let us take the origin of the coordintes plane as the vertex of the parabola, so the vertical axis is along the positive y - axis.

This is as shown in the figure.

According to the fig, AB and 0C are the longest and shortest wires attached to the cable respectively. LM is the supporting wire attached to the roadway, 18 m away from the middle.

Given AB = 30 m, 0C = 6m and BC = 1002=50m

Step 2 :

The equation of the parabola is of the form x2=4ay

The coordinates of the point A are (50, (30-6) ) (i.e) (50, 24)

Substituting this for x and y in the equation of the parabola,

(50)2=4a(24)

⇒a=50×504×24=62524

Step 3 :

Hence equation of the parabola is

x2=4(62524)y

(.e) x2=6256y

⇒6x2=625y

Step 4 :

The x coordinates at point D is 18.

at x = 18

6(18)2=625y

∴y=6×18×18625

=3.11 ( approx )

∴LP=3.11m

But LM = LP + PM

= 3.11 + 6

$ = 9.11 m

Hence the length of the supporting wire attached to the roadway 18m from the middle is 9.11 m approx.

Answer 2

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