Ques-3) A cyalist goes around a circular track
Once
every
2 minutes If the radius of
the circular track is 105 m, calculate
a) distance after 3/4 of the cycle
b) displacement after 3/4 of the cycle
Solve-
Answers
Answer:
a)495m, b)178.5m
Explanation:
Radius of circular track, r = 105 m
Time taken, t = 2 min
= 2 × 60
= 120 s
Circumference of circular track = 2πr
⇒ Circumference = 2 × 22/7 × 105
⇒ Circumference = 660 m
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a) Distance after 3/4 of cycle = (3/4) of circular track
⇒Distance = (3/4) 660
⇒Distance = 1980/4
⇒Distance = 495m
b) Displacement after 3/4 of cycle = Length of chord subtended by radii at 90° with each other = 2r sin (θ/2)
⇒ Displacement = 2 × 105 × sin (90/2)
⇒ Displacement = 210 × sin 45
⇒ Displacement = 210 × (1/√2)
⇒ Displacement = 210 × 0.85
⇒ Displacement = 178.5m
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∴ After 3/4th of the cycle,
Distance = 495m and Displacement = 178.5m
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