Answer:
The kinetic energy of the sled is going to increase by 18.75%
Step-by-step explanation:
The work W realized by a Force F is given by:
![W=F_x*x](https://tex.z-dn.net/?f=W%3DF_x%2Ax)
Where x is the displacement and
is the component of the force that is parallel to the displacement.
Additionally, the work is equal to the change in the kinetic energy
![W=K_f-K_i](https://tex.z-dn.net/?f=W%3DK_f-K_i)
If your pulling force is in the same direction as the sled's displacement, we can said that: ![F=F_x](https://tex.z-dn.net/?f=F%3DF_x)
And if increases the kinetic energy of the sled by 27%, we can said that:
![K_f-K_i=0.27K_i](https://tex.z-dn.net/?f=K_f-K_i%3D0.27K_i)
So, we can formulate the following equation:
(1)
On the other hand, if the pulling force acted at an angle of 46° above the horizontal, the work is:
(2)
Then, replacing (1) in (2), we get:
![W=F*x*cos(46)=0.27K_i*cos(46) = 0.1875K_i](https://tex.z-dn.net/?f=W%3DF%2Ax%2Acos%2846%29%3D0.27K_i%2Acos%2846%29%20%3D%200.1875K_i)
Finally, the kinetic energy increase by 18.75% because:
![W=K_f-K_i\\W=0.1875K_i\\\\K_f-K_i=0.1875K_i](https://tex.z-dn.net/?f=W%3DK_f-K_i%5C%5CW%3D0.1875K_i%5C%5C%5C%5CK_f-K_i%3D0.1875K_i)