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Chapter 1: Q68P (page 1)

An iceboat is at rest on a frictionless frozen lake when a sudden wind exerts a constant force of 200 N, toward the east, on the boat. Due to the angle of the sail, the wind causes the boat to slide in a straight line for a distance of 8.0 m in a direction 20 north of east. What is the kinetic energy of the iceboat at the end of that 8.0 m?

Short Answer

Expert verified

The kinetic energy (K.E) of the iceboat is 1.5 kJ.

Step by step solution

01

Given information

It is given that,

  1. The force exerted on the iceboat isF=200N

The displacement of the iceboat isd=8.0 in the direction 20 degrees north of east

02

Determining the concept

This problem deals with the work-energy theorem which states that the net work done by the forces applied on object is equal to the change in its kinetic energy. Find the work done by the wind from the force using the corresponding formula. Then using the work-energy theorem, find the kinetic energy (K.E) of the iceboat.

Formulae:

W=F.d=Fdcosθ

Work-energy theorem givesW=K.E.

Where,

F is force, dis displacement, K.E. is change in kinetic energy and Wis the work done.

03

determining the kinetic energy (K.E) of the iceboat

The work done by the wind on the iceboat is,

W=Fdcosθ=2008cos20°W=1504J≈1.5kJ

Work energy theorem gives,W=K.E

K.E=1504J

Therefore, the kinetic energy (K.E) of the iceboat is1.5kJ.

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