Here are the positions at three different times for a bee in flight (a bee\'s to

Question

Here are the positions at three different times for a bee in flight (a bee's top speed is about 7 m/s) Time 5.0 s 5.3 s Position.9,a.o, o) m04, 7,0) m (0.7,5.7,0)m (a) Between 4.7·and S.O s, what was the bee's average velocity? Be careful with signs. mVs (b) Between 4.7 s and 5.3 s, what was the bee's average velocity? Be careful with signs m's (c) Of the two average velocities you calculated, which is the best estimate of the bee's instantaneous velocity at time 4.7 s d) Using the best information avalable, what was the displacement of the bee during the time l tral from 47·to 47e Additional Materials Section 1.6

Explanation / Answer

given
bee's top speed V = 7 m/s

position at 4.7 s, r1 = (-1.9,8,0) m
position at 5.0 s, r2 = (-0.4,7,0) m
position at 5.3 s, r3 = (0.7,5.7,0) m

a) between 4.7 s to 5 s
   displacement = r2 - r1 = (1.5,-1,0)
   displacement magnitude = |r2 - r1| = sqroot(1.5^2 + 1) = 1.80277 m
   average velocity = (1.5,-1,0)/0.3 = (5,-3.333,-0) m/s
   average velocity magnitude = 6.009 m/s

b) between 4.7 s to 5.3 s
   displacement = r3 - r1 = (2.6,-2.3,0)
   displacement magnitude = |r3 - r1| = sqroot(2.6^2 + 2.3^2) = 3.4713 m
   average velocity = (2.6,-2.3,0)/0.6 = (4.33,-3.833,-0) m/s
   average velocity magnitude = 5.785 m/s
c) the best estimate of the velocity at t = 4.7 s is the one taken by averaging till time 5 s because it considers less amouint of time and hence is closer to instantaneous velocity
   so, option a) gives the closest estimate towards the instantaneous velocity at time 4.7 s
d) dispacement = velocity * time
   using velocity from the last part
   displacement = 6.009*(4.75-4.7) = 0.30045 m

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