Question

A novice golfer on the green takes three strokes to sink the ball. The successive displacements are 4.00 m to the north, 2.20 m northeast, and 1.10 m at 25.0° west of south. Starting at the same initial point, an expert golfer could make the hole in what single displacement?

Answer 1

we can solve this question using the cordinate geometry

Taking North as +'ve Y-axis and South as -'ve Y -axis

           East as +'ve X-axis and West as -'ve X -axis

We will follow the cordinate of ball after each displacement

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1st Move - 4.00 m to the North

       so the cordinate of ball after this movement will be

                     P1 = (0,4)

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2nd Move - 2.20 m toward Northeast that is at angle 45 degree and magnitude of 2.20 m

so X movement will be

      DCos45= 2.20*Cos45 = 1.56 m

   and Y movement will be

DSin45= 2.20*Sin45 = 1.56 m

after this the Cordinate of the ball will be

     P2 = (0+1.56, 4+1.56)

     P2 = (1.56, 5.56)

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3rd Move - 1.10 m at angle 25.0 degree west of south

so X movement will be

      -DSin25= 1.10*Sin25 = -0.46 m

   and Y movement will be

-DCos25= -1.10*Cos25 = -1.00 m

after this the Cordinate of the ball will be at

P3 = (1.56-0.46, 5.56-1.00)

P3 = (1.10, 4.56)

Now since the final position of the ball after all three successive displacement is (1.10,4.56) So now we can calculate the magnitude and direction of it for one single displacement

So the direction will be East of North

For expert single displacment has to be 4.70 m in direction of 13.56 degree East of North