11. In a cricket match, a batsman hits a ball into the air which is moving in a parabolic path. This curved path
followed by the ball forms a parabola. Parabola is represented by a polynomial. If the polynomial represent the
height covered is f(t) = -2 + 15t-7
Answers
Given : a cricket match, a batsman hits a ball into the air which is moving in a parabolic path.
This curved path followed by the ball forms a parabola.
Parabola is represented by a polynomial.
the polynomial represent the height covered is f(t) = –2t²+ 15t – 7
To Find: Maximum height
Solution:
f(t) = –2t²+ 15t – 7
=> f'(t) = -4t + 15
f'(t) = 0
=> -4t + 15 = 0
=> t = 15/4
f''(t) = - 4 < 0
Hence maximum height at t = 15/4
max height = –2( 15/4)²+ 15(15/4) – 7
= -225/8 + 225/4 - 7
= 225/8 - 7
= 169/8
= 21.125
Maximum height = 169/8 = 21.125
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