A speedboat with a length of 10.2m and a mass of 215 kg is negotiaging a circula

Question

A speedboat with a length of 10.2m and a mass of 215 kg is negotiaging     a circular turn (radius = 32 m) around a buoy.  During the turn, the     engine causes a net tangential force of magnitude 558 N to be applied to    the boat. The intial speed of the boat going into the turn is 4 m/sec.

1) What is the tangential acceleration of the boat, 2 sec into the turn?       

aT = _______ m/sec^2

2) What is the tangential velocity of the boat, 2 sec into      the turn?       

vT = _________ m/sec

3) What is the centripetal acceleration, 2 sec into the turn?       

acen = ________ m/sec^2

4) What is the total acceleration, 2 sec into the turn?       

a = ____________ m/sec^2

Explanation / Answer

a) a = F/m
     = 558N / 215kg
     = 2.59 m/s^2

b) v(t) = v0 + at
        = 4m/s + 2.59 m/s^2*2s
        = 9.18 m/s

c) centripeta acc. = v^2/r
                   = (9.18 m/s)^2/32m
                   = 2.63 m/s^2

d) atotal = sqrt[2.59^2+2.63^2]
          = 3.69 m/s^2

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