Fsc Part 2 Mathematics (Complete Solutions)

Q6
A stone falls from a height of 60m on the ground, the height h after x second is approximately given by

h(x) = 40 - 10x2
(i)       What is the height of the stone when:
(a)     x = 1 sec?            (b)     x = 1.5 sec?            (c)     x = 1.7 sec?
(ii) When does the stone strike the ground?

Solution:

Given     h(x) = 40 - 10x2

(i) What is the height of the stone when:
(a)     x = 1 sec?
h(1) = 40 - 10(1)2
h(1) = 40 - 10
h(1) = 30 m

(b)     x = 1.5 sec?
h(1.5) = 40 - 10(1.5)2
h(1.5) = 40 - 10(2.25)
h(1.5) = 40 - 22.5
h(1.5) = 17.5 m

(b)     x = 1.7 sec?
h(1.7) = 40 - 10(1.7)2
h(1.7) = 40 - 10(2.89)
h(1.7) = 40 - 28.9
h(1.7) = 11.1 m


(ii) When does the stone strike the ground?
h(x) = 0
40 - 10x2 = 0
10x2 = 40
x2 = 4
x = ±2

Stone strike the ground after 2 sec.

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