A stone is thrown vertically upwards such that its height is S metres above the ground after t seconds is given by s = 40t - 10t². Find

A stone is thrown vertically upwards such that its height is S metres above the ground after t seconds is given by s = 40t - 10t².
Find
i) The height above the ground after 2 seconds
ii) The velocity after 1 second
iii) The instant at which the stone is 30 m high

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i) Height above the ground

after 2 seconds is

s = 40t - 10t².

s = 40 x 2 - 19(2)t².

s = 80 - 40

s = 40 metres

ii) Velocity = $\frac{ds}{dt}$ = 40 - 20t

At t = 1 second

$\frac{ds}{dt}$ = 40 - 20

= 20 m/s


iii) The instance at which the stone is 30 m height

40t - 10t². = 30

-10t² + 40t + 30 = 0

10t² - 40t + 30 = 0

t² - 4t + 3 = 0

P = 3; S = -4; N = -3, -1

(t² - 3t)-(t + 3)= 0

t(t - 3) -1(t + 3) = 0

(t - 1)(t - 3) = 0

t = 1 sec or t = 3 sec

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johnmulu answered the question on March 8, 2017 at 05:55

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