Question

a cyclist travels 3/4 of a circular track from A to B radius of circular track is 400m what is distance travelled by a cyclist and what i diplacement

Answer 1

The distance travelled by the cyclist is 1885.71m and displacement is 565.68 m.

Given:

The above problem can be solved by using the following formula,

Distance from A to B = 400m

Distance covered by cyclist $=\frac{3}{4}$

Total distance = circumference (2π radius)

$\pi=\frac{22}{7}$

$Total\ distance =2 \times \frac{22}{7} \times 400=2514.28$

Distance covered by the cyclist $=\frac{3}{4}=75 \%=\frac{75}{100} \times 2514=1885.71 m$

Displacement $=\sqrt{400^{2}}+\sqrt{400^{2}}$

By using Pythagoras theorem,

$\mathrm{h}(\text {displacement})^{2}=\mathrm{R}_{1}(\text { radius })^{2}+\mathrm{R}_{2}(\text { radius })^{2}\\ \Rightarrow h^{2}=400^{2}+400^{2} \Rightarrow h^{2}=160000$

$\Rightarrow h=565.68 \mathrm{m}$

Therefore, the distance travelled by the cyclist is 1885.71m and displacement is 565.68 m .

Answer 2

Answer:

Known Terms:-

r = Radius

s = Distance

Given:-

Radius of the circular track = 400 m

Distance traveled by cyclist =  of a circular track.

To Find:-

Displacement by the cyclist

Formula to be used:-

Circumference that is 2πr

Solution:-

Circumference of a $\frac{3}{4}$ circle

= $\frac{3}{4}$ × 2πr

= $\frac{3}{4}$ × 2 × $\frac{22}{7}$ × 400

= 1885.71 metres

Hence, displacement by cyclist is 1885.71 m.