Question

A speedboat with a length of 10.2m and a mass of 217 kg is negotiaging a circular turn (radius = 34 m) around a buoy. During the turn, the engine causes a net tangential force of magnitude 526 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 Submit 2) What is the tangential velocity of the boat, 2 sec into the turn? VT Submit m/sec 3) What is the centripetal acceleration, 2 sec into the turn? acen m/sec2 Submit 4) What is the total acceleration, 2 sec into the turn? a - m/sec2 Submit

Answer 1

Solution)

1) We know-

Force, F = ma

So,

Acceleration, at = F/m = 526 N/217 kg= 2.42 m/s^2

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2)

We know, v = u+at

So,

Tangential velocity, v= 4+2.42*2 = 9.87 m/s

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3)

Centripetal Acceleration, ac = v^2/r = 9.87^2/34 m = 2.86 m/s^2

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4)

Total Acceleration,

a = sqrt(at^2+ac^2)

a = 3.75 m/s^2

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