You pull a sled across a horizontal frictionless patch of snow. If your pulling force is in the same direction as the sled's displacement and increases the kinetic energy of the sled by 27%, by what percentage would the sled's kinetic energy increase if the pulling force acted at an angle of 46° above the horizontal?

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:[tex]W=F_x*x[/tex]Where x is the displacement and [tex]F_x[/tex] is the component of the force that is parallel to the displacement.Additionally, the work is equal to the change in the kinetic energy [tex]W=K_f-K_i[/tex]If your pulling force is in the same direction as the sled's displacement, we can said that: [tex]F=F_x[/tex]And if increases the kinetic energy of the sled by 27%, we can said that:[tex]K_f-K_i=0.27K_i[/tex]So, we can formulate the following equation:[tex]W=F*x\\W=0.27K_i\\\\F*x=0.27K_i[/tex] (1)On the other hand, if the pulling force acted at an angle of 46° above the horizontal, the work is:[tex]W=F_x*x=Fcos(46)*x=F*x*cos(46)[/tex]   (2)Then, replacing (1) in (2), we get:[tex]W=F*x*cos(46)=0.27K_i*cos(46) = 0.1875K_i[/tex]Finally, the kinetic energy increase by 18.75% because:[tex]W=K_f-K_i\\W=0.1875K_i\\\\K_f-K_i=0.1875K_i[/tex]