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Question-72560

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Question Number 72560 by Umar last updated on 30/Oct/19
Commented by Umar last updated on 30/Oct/19
solve 3 and 4 pls
$$\mathrm{solve}\:\mathrm{3}\:\mathrm{and}\:\mathrm{4}\:\mathrm{pls} \\ $$
Commented by TawaTawa last updated on 30/Oct/19
(3i) We have, u = 10m/s, v = 15m/s, a = 1m/s^2 . The time (t) = ? a = ((v − u)/t) ∴ 1 = ((15 − 10)/t) ∴ t = 5s (3ii) v^2 = u^2 + 2as ∴ 15^2 = 10^2 + 2(1)s ∴ 225 = 100 + 2s ∴ 2s = 225 − 100 ∴ 2s = 125 ∴ s = ((125)/2) ∴ s = 62.5m (3iii) s = (((v + u)/2)).t ∴ v^2 = u^2 + 2as ∴ v^2 = 0^2 + 2(1)(100) ∴ v^2 = 0 + 200 ∴ v^2 = 200 ∴ v = (√(200)) ∴ v = 14.14 m/s
$$\left(\mathrm{3i}\right) \\ $$$$\mathrm{We}\:\mathrm{have},\:\:\:\:\:\:\mathrm{u}\:\:=\:\:\mathrm{10m}/\mathrm{s},\:\:\:\:\:\:\:\:\mathrm{v}\:\:=\:\:\mathrm{15m}/\mathrm{s},\:\:\:\:\:\mathrm{a}\:\:=\:\:\mathrm{1m}/\mathrm{s}^{\mathrm{2}} . \\ $$$$\mathrm{The}\:\mathrm{time}\:\left(\mathrm{t}\right)\:\:=\:\:? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\mathrm{a}\:\:=\:\:\frac{\mathrm{v}\:−\:\mathrm{u}}{\mathrm{t}} \\ $$$$\therefore\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{1}\:\:=\:\:\frac{\mathrm{15}\:\:−\:\mathrm{10}}{\mathrm{t}} \\ $$$$\therefore\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{t}\:\:=\:\:\mathrm{5s} \\ $$$$\left(\mathrm{3ii}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{v}^{\mathrm{2}} \:\:=\:\:\mathrm{u}^{\mathrm{2}} \:+\:\mathrm{2as} \\ $$$$\therefore\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{15}^{\mathrm{2}} \:\:=\:\:\mathrm{10}^{\mathrm{2}} \:+\:\mathrm{2}\left(\mathrm{1}\right)\mathrm{s} \\ $$$$\therefore\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{225}\:\:=\:\:\mathrm{100}\:+\:\mathrm{2s} \\ $$$$\therefore\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2s}\:\:\:=\:\:\:\mathrm{225}\:−\:\mathrm{100} \\ $$$$\therefore\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2s}\:\:\:=\:\:\:\mathrm{125} \\ $$$$\therefore\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{s}\:\:=\:\:\frac{\mathrm{125}}{\mathrm{2}} \\ $$$$\therefore\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{s}\:\:=\:\:\mathrm{62}.\mathrm{5m} \\ $$$$\left(\mathrm{3iii}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{s}\:\:=\:\:\left(\frac{\mathrm{v}\:+\:\mathrm{u}}{\mathrm{2}}\right).\mathrm{t} \\ $$$$\therefore\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{v}^{\mathrm{2}} \:\:=\:\:\mathrm{u}^{\mathrm{2}} \:+\:\mathrm{2as} \\ $$$$\therefore\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{v}^{\mathrm{2}} \:\:=\:\:\mathrm{0}^{\mathrm{2}} \:+\:\mathrm{2}\left(\mathrm{1}\right)\left(\mathrm{100}\right) \\ $$$$\therefore\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{v}^{\mathrm{2}} \:\:=\:\:\mathrm{0}\:+\:\mathrm{200} \\ $$$$\therefore\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{v}^{\mathrm{2}} \:\:=\:\:\:\mathrm{200} \\ $$$$\therefore\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{v}\:\:=\:\:\:\sqrt{\mathrm{200}} \\ $$$$\therefore\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{v}\:\:=\:\:\:\mathrm{14}.\mathrm{14}\:\mathrm{m}/\mathrm{s} \\ $$$$ \\ $$
Commented by TawaTawa last updated on 30/Oct/19
(4) v^2 = u^2 + 2as ∴ 20^2 = 50^2 + 2(− 10).s ∴ 400 = 2500 − 20s ∴ 400 − 2500 = − 20s ∴ − 2100 = − 20s ∴ s = ((− 2100)/(− 20)) ∴ s = 105m
$$\left(\mathrm{4}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{v}^{\mathrm{2}} \:\:=\:\:\mathrm{u}^{\mathrm{2}} \:+\:\mathrm{2as} \\ $$$$\therefore\:\:\:\:\:\:\:\:\mathrm{20}^{\mathrm{2}} \:\:=\:\:\mathrm{50}^{\mathrm{2}} \:+\:\mathrm{2}\left(−\:\mathrm{10}\right).\mathrm{s} \\ $$$$\therefore\:\:\:\:\:\:\:\:\mathrm{400}\:\:\:=\:\:\:\mathrm{2500}\:\:−\:\:\mathrm{20s} \\ $$$$\therefore\:\:\:\:\:\:\:\:\mathrm{400}\:\:\:−\:\:\mathrm{2500}\:\:=\:\:−\:\:\mathrm{20s} \\ $$$$\therefore\:\:\:\:\:\:\:\:−\:\:\mathrm{2100}\:\:=\:\:−\:\:\mathrm{20s} \\ $$$$\therefore\:\:\:\:\:\:\:\:\:\:\:\mathrm{s}\:\:\:=\:\:\frac{−\:\mathrm{2100}}{−\:\mathrm{20}} \\ $$$$\therefore\:\:\:\:\:\:\:\:\:\:\:\mathrm{s}\:\:\:=\:\:\mathrm{105m} \\ $$
Commented by TawaTawa last updated on 30/Oct/19
Sir MrW please check.
$$\mathrm{Sir}\:\:\mathrm{MrW}\:\:\mathrm{please}\:\mathrm{check}. \\ $$
Commented by Umar last updated on 30/Oct/19
Thank u sir
$$\mathrm{Thank}\:\mathrm{u}\:\mathrm{sir} \\ $$

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