Tamil Nadu Board of Secondary EducationHSC Arts Class 12

# On lighting a rocket cracker it gets projected in a parabolic path and reaches a maximum height of 4 m when it is 6m away from the point of projection. Finall - Mathematics

Sum

On lighting a rocket cracker it gets projected in a parabolic path and reaches a maximum height of 4 m when it is 6m away from the point of projection. Finally it reaches the ground 12 m away from the starting point. Find the angle of projection

#### Solution

Equation of the parabola be x2 = – 4ay  .......(1)

B(6, – 4) lies on parabola

62 = – 4a(– 4)

36/16 = a

⇒ a = 9/4

(1) ⇒ x2 = - (9/4) y

x2 = – 9y  .......(2)

Now need tofind slope at (– 6, – 4)

Diff (2) w.r.to x

2x = - 9  ("d"y)/("d"x)

("d"y)/("d"x) = (2x)/(-9)

At(– 6, – 4), ("d"y)/("d"x) = (2(- 6))/(- 9)

= 12/9

= 4/3

tan θ = 4/3

θ = tan^-1 (4/3)

Concept: Real Life Applications of Conics
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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 9 | Page 215
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