Fsc Part 2 Mathematics (Complete Solutions)

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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 - 10x

^{2}(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 - 10x

^{2}(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 - 10x

^{2}= 010x

^{2}= 40x

^{2}= 4x = ±2

Stone strike the ground after 2 sec.