Answer
$50\sqrt{2}=70.71N$
Work Step by Step
It is given that a force of $100N$ is applied in the vertical direction, making angle of $45^{\circ}$ with the ground.
We care about the horizontal component, for the lawn mower must move in the horizontal direction.
$F=100\cos{45^\circ}=\frac{100}{\sqrt{2}}=50\sqrt{2}=70.71N$
