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Question Number 111549 by Study last updated on 04/Sep/20
a car has a tire diameter of 0.5m and a speed of ((80km)/(hr)) so how many cycles will this car hit in 3 minutes?
$${a}\:{car}\:{has}\:{a}\:{tire}\:{diameter}\:{of}\:\mathrm{0}.\mathrm{5}{m}\:{and} \\ $$$$\:{a}\:{speed}\:{of}\:\frac{\mathrm{80}{km}}{{hr}}\:{so}\:{how}\:{many}\:{cycles}\: \\ $$$${will}\:{this}\:{car}\:{hit}\:{in}\:\mathrm{3}\:{minutes}? \\ $$
Answered by Lordose last updated on 04/Sep/20
v=(s/t)=((80km)/(1hr))=((80000)/(3600))=22.2m/s t=3mins=3×60s=180s s=vt s=((800)/(36))×180=4000m 1 complete cycle=2𝛑r m i.e 2×0.25𝛑=1cycle 4000m=x cycles x=((4000)/(0.5𝛑))=((8000)/𝛑)cycles
$$\boldsymbol{\mathrm{v}}=\frac{\boldsymbol{\mathrm{s}}}{\boldsymbol{\mathrm{t}}}=\frac{\mathrm{80}\boldsymbol{\mathrm{km}}}{\mathrm{1}\boldsymbol{\mathrm{hr}}}=\frac{\mathrm{80000}}{\mathrm{3600}}=\mathrm{22}.\mathrm{2}\boldsymbol{\mathrm{m}}/\boldsymbol{\mathrm{s}} \\ $$$$\boldsymbol{\mathrm{t}}=\mathrm{3}\boldsymbol{\mathrm{mins}}=\mathrm{3}×\mathrm{60}\boldsymbol{\mathrm{s}}=\mathrm{180}\boldsymbol{\mathrm{s}} \\ $$$$\boldsymbol{\mathrm{s}}=\boldsymbol{\mathrm{vt}} \\ $$$$\boldsymbol{\mathrm{s}}=\frac{\mathrm{800}}{\mathrm{36}}×\mathrm{180}=\mathrm{4000}\boldsymbol{\mathrm{m}} \\ $$$$\mathrm{1}\:\boldsymbol{\mathrm{complete}}\:\boldsymbol{\mathrm{cycle}}=\mathrm{2}\boldsymbol{\pi\mathrm{r}}\:\boldsymbol{\mathrm{m}} \\ $$$$\boldsymbol{\mathrm{i}}.\boldsymbol{\mathrm{e}}\:\mathrm{2}×\mathrm{0}.\mathrm{25}\boldsymbol{\pi}=\mathrm{1}\boldsymbol{\mathrm{cycle}} \\ $$$$\:\mathrm{4000}\boldsymbol{\mathrm{m}}=\boldsymbol{\mathrm{x}}\:\boldsymbol{\mathrm{cycles}} \\ $$$$\boldsymbol{\mathrm{x}}=\frac{\mathrm{4000}}{\mathrm{0}.\mathrm{5}\boldsymbol{\pi}}=\frac{\mathrm{8000}}{\boldsymbol{\pi}}\boldsymbol{\mathrm{cycles}} \\ $$
Answered by nimnim last updated on 04/Sep/20
Circumference of the wheel=DĪ€=0.5Ī€.m Speed=80×((1000)/(60)) m/min Distance covered in 3min=80×((1000)/(60))×3.m =4000m Req. no of revolution=((4000)/(0.5Ī€)) =8000×(7/(22))=2545(5/(11))≈
$$\mathrm{Circumference}\:\mathrm{of}\:\mathrm{the}\:\mathrm{wheel}=\mathrm{D}\pi=\mathrm{0}.\mathrm{5}\pi.{m} \\ $$$$\mathrm{Speed}=\mathrm{80}×\frac{\mathrm{1000}}{\mathrm{60}}\:{m}/\mathrm{min} \\ $$$$\mathrm{Distance}\:\mathrm{covered}\:\mathrm{in}\:\mathrm{3min}=\mathrm{80}×\frac{\mathrm{1000}}{\mathrm{60}}×\mathrm{3}.{m} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{4000}{m} \\ $$$$\mathrm{Req}.\:\mathrm{no}\:\mathrm{of}\:\mathrm{revolution}=\frac{\mathrm{4000}}{\mathrm{0}.\mathrm{5}\pi} \\ $$$$\:\:=\mathrm{8000}×\frac{\mathrm{7}}{\mathrm{22}}=\mathrm{2545}\frac{\mathrm{5}}{\mathrm{11}}\approx \\ $$

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