# A block is pushed up a frictionless inclined plane as shown below.Determine the magnitude of the horizontal force vector,F=|F|,that will keep the block sliding up the incline with a constant velocity :

$\begin{array}{1 1}mg\sin\theta\\mg\cos\theta\\mg\tan\theta\\mg\cot\theta\end{array}$

Answer : $mg\tan\theta$
To push the block up the inclined plane at a constant velocity, there must be no net force on the block along the direction of the incline.
Therefore the component of F along the incline must cancel the component of the weight along the incline.
This cancellation implies that $F cos\theta = mg \sin\theta$ or $F = mg \tan \theta$.