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I don't know why I am getting a different answer but here is the question:

A toboggan is initially moving at a constant velocity along a snowy horizontal surface. Ignore friction. When a pulling force is applied parallel to the ground over a certain distance, the kinetic energy increases by 47%. By what percentage would the kinetic energy have changed if the pulling force had been at an angle of 38° above the horizontal?

A few things:

Ekf = Final kinetic energy

Eki = Initial kinetic energy

m=mass

vf=final velocity

vi=initial velocity

Now:

Case 1 (where the force applied is parallel to the ground)

2Facos0(mvf-mvi)=2(100 x 0.47)

mvf-mvi=(100 x 0.47)/Fa

Case 2 (where the force is at 38° to the horizontal)

2Facos38(mvf-mvi)=2(100 x y)

mvf-mvi= (100 x y )/FaCos38

Now equating the two equations:

100 x 0.47 = (100 x y)/cos38

Solving for y I got y=0.37

So the increase is ~ 10%, and the answer is 16%. What did I do wrong?

A toboggan is initially moving at a constant velocity along a snowy horizontal surface. Ignore friction. When a pulling force is applied parallel to the ground over a certain distance, the kinetic energy increases by 47%. By what percentage would the kinetic energy have changed if the pulling force had been at an angle of 38° above the horizontal?

A few things:

Ekf = Final kinetic energy

Eki = Initial kinetic energy

m=mass

vf=final velocity

vi=initial velocity

Now:

Case 1 (where the force applied is parallel to the ground)

2Facos0(mvf-mvi)=2(100 x 0.47)

mvf-mvi=(100 x 0.47)/Fa

Case 2 (where the force is at 38° to the horizontal)

2Facos38(mvf-mvi)=2(100 x y)

mvf-mvi= (100 x y )/FaCos38

Now equating the two equations:

100 x 0.47 = (100 x y)/cos38

Solving for y I got y=0.37

So the increase is ~ 10%, and the answer is 16%. What did I do wrong?

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