Question

A cyclist goes around a circular track once every 60 seconds. If the radius of the circular track is 105m, calculate the speed.​

Answer 1

Anѕwєr :

11 m/s

Explαnαtion :

As per the provided information in the given question, we have :

• Radius of the track, r = 105 m
• Time taken, t = 60 seconds

We've been asked to calculate the speed of the cyclist.

⠀⠀⠀⠀⠀⠀⠀⠀⠀» According to the question, we have radius of the track and time taken. Speed can be calculated only when we have distance covered and time taken. So, basically firstly we need to calculate the total distance covered.

Total distance covered will be the the total length of the circular track and as we have the value of radius, so we can calculate the total length of the circular track using the formula of circumference of the track.

$\Large {\underline { \sf {Distance \; covered:}}}$

$\dashrightarrow\sf{Distance \; covered = Total \; length_{(Track)}}$

$\dashrightarrow\sf{Distance \; covered = Circumference_{(Track)}}$

$\dashrightarrow\sf{Distance \; covered = 2\pi r}$

$\dashrightarrow\sf{Distance \; covered = 2\times \dfrac{22}{7} \times 105 \; m}$

$\dashrightarrow\sf{Distance \; covered = \dfrac{44}{7} \times 105 \; m}$

$\dashrightarrow\sf{Distance \; covered = 44 \times 15 \; m}$

$\dashrightarrow \underline{\textbf{\textsf{Distance \; covered = 660 \; m}}}$

Now, finding out the speed of the cyclist.

$\dashrightarrow \boxed{\sf{Speed = \dfrac{Distance}{Time}}}$

$\dashrightarrow\sf{Speed = \dfrac{660 \; m}{60 \; s} }$

$\dashrightarrow \underline{\boxed{\textbf{\textsf{Speed}} =\textbf{\textsf{11}} \; \textbf{\textsf{m\: s}}^{\textbf{\textsf{-1}}} }}$

∴ Speed of the cyclist is 11 m/s.

Answer 2

Given :

r = 105 m

t = 60 seconds

To find :

the speed of the cyclist.

Solution :

Total distance covered = the total length of the circular track

Distance covered = 2πr

Distance covered = 2 × 22/7 × 105 m

Distance covered = 44/7 × 105 m

Distance covered = 44 × 15 m

Distance covered = 660 m

Speed of the cyclist = Distance / Time taken = 660m / 60s

Speed = 11m/s

∴ Speed of the cyclist is 11 m/s.