Tamil Nadu Board of Secondary EducationHSC Arts Class 12

# Assume that water issuing from the end of a horizontal pipe, 7 5. m above the ground, describes a parabolic path. The vertex of the parabolic path is at the end of the pipe. At a position 2 5. m - Mathematics

Sum

Assume that water issuing from the end of a horizontal pipe, 7 5. m above the ground, describes a parabolic path. The vertex of the parabolic path is at the end of the pipe. At a position 2 5. m below the line of the pipe, the flow of water has curved outward 3 m beyond the vertical line through the end of the pipe. How far beyond this vertical line will the water strike the ground?

#### Solution

Equation of the water path is

x2 = – 4 ay

Use the point (3, – 2.5) in (1)

(3)2 = – 4a(– 2.5)

9 = 10a

a = 9/10 substituting in (1)

(1) ⇒ x2 = - 4  9/10 y ........(2)

Use the point (x1, – 7.5) in (2)

(2) ⇒ x12 = - 4 9/10(- 7.5)

⇒ x12 = 30(9/10)

x1 = sqrt(3 xx 9)

x1 = 3sqrt(3)  "m"

∴ The water strikes the ground  3sqrt(3)  "m" beyond the vertical line.

Concept: Real Life Applications of Conics
Is there an error in this question or solution?
Chapter 5: Two Dimensional Analytical Geometry-II - Exercise 5.5 [Page 215]

#### APPEARS IN

Tamil Nadu Board Samacheer Kalvi Class 12th Mathematics Volume 1 and 2 Answers Guide
Chapter 5 Two Dimensional Analytical Geometry-II
Exercise 5.5 | Q 8 | Page 215
Share