The graph below shows the position functions, x(t), for a runner that is running

Question

The graph below shows the position functions, x(t), for a runner that is running at constant velocity, m/s, and a bus that is slowly accelerating, m/s^2. (a) At what approximate time does the runner pass the bus? (b) And when the bus passes the runner? (c) At what point in time do the runner and the bus have the same approximate instantaneous velocity? (d) Approximately how long could the runner delay starting and still just barely catch the bus once? A boat can travel 2.90 m/s in still water. (a) If the boat points directly across a stream whose current is 2.10 m/s, what is the velocity of the boat relative to the shore (give both the magnitude and angle the velocity vector makes with the shore. (b) If the stream is 20 m wide, how long will it take the boat to cross? A giant vertical wheel is 40 m in diameter, and is fitted with a cage and platform on which a person can stand. The mass of the person inside the cage is 75 kg. (a) What velocity must the wheel rotate for the man inside the cage at location X, as shown, to not exert any force on the cage? (b) And the velocity of the wheel for the man to exert five times his weight on the cage at location X?

Explanation / Answer

(5) ans

Given that

velocity of the boat in water Vbw=2.9 m/s

velocity of water w.r.to ground Wwg=2.1 m/s

now we find the velocity boat w.r.to ground

velocity of boat w.r.to ground Vbg=[2.9^2-2.1^2]^1/2=2 m/s

angle=cos^-1[2/2.9]=46.4 degree

now we find the time to cross the river

time t=20/2=10 sec

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6 ans

Given that

diameter D=40 m

radius r=10 m

mass m=75 kg

now we find the velocity inside

velocity V=[2gr]^1/2=[2*9.8*10]^1/2=14 m/s

now we find the velocity after mass in creases 5 times

m1/m2=v2^2/v1^2

m/5m=v2^2/14^2

196/5=v2^2

velocity V2=6.3 m/s

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