An athelete of mass 80 kg is running on a rough track whose cross-section is shown below. The lower part AB of track is a cylindrical valley of radius 100 m and upper part BC is a cylindrical hill of radius 200 m. The two parts join such that there is no sudden change of slope of the track. The speed of the athelete on the track is always 5m/s. A is the lowest point of the valley, B is the point at which valley ends and hill starts and C is the top of the hill. While moving from A to C, the athelete travels a horizontal distance of 150 m.

Linked Question 1

Find the time taken by the athelete in going from A to C

20π sec

10π sec

5π sec

15π sec

S_AC = S_AB + S_BC
= R₁ $(\frac{π}{6})$ + R₂ $(\frac{π}{6})$
= $(\frac{100}{6} + \frac{200}{6}) π$
S_AC = $\frac{300}{6} π$ = 50 π m
t = $\frac{S_{AC}}{V} = \frac{50 π}{5}$ = 10 π s

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Linked Question 2

The correct order of normal force experienced by athelete is :

N_A > N_B > N_C

N_A > N_C > N_B

N_C > N_A > N_B

N_A < N_B < N_C

N_A – mg = $\frac{{mv}^{2}}{R_{1}}$ Similarly N_B = mgcosθ = mg $\frac{\sqrt{3}}{2}$ = m(8.66)
N_A = mg + $\frac{{mv}^{2}}{R_{1}} m (g + \frac{V^{2}}{R_{1}})$ = m(10.5) & N_C = mg – $\frac{{mv}^{2}}{R_{2}} = m (g - \frac{V^{2}}{R_{2}})$ = m(9.75)
⇒ (N_A > N_C > N_B )

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Linked Question 3

The magnitude of friction force experienced by the athelete is :

decreases continuously during motion from A to C

attains a maximum value at B

zero throughout

increases continuously from A to C

Since v is constant

Hence tangential acceleration = 0

⇒ f_S = mgsinθ
⇒ f_A < f_B < f_C

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