(a) While trying to pull a cart, a horse pushes the ground backwards with a certain force at an angle. The ground offers an equal reaction in opposite direction; on the feet of the horse. The forward component of this reaction is responsible for the motion of cart.
In empty space, there is no reaction and hence horse cannot pull the cart and run.
(b) This is due to inertia of motion possessed by the passengers in a speeding bus.
(c) Consider the free body diagram in the two cases, the lawn mover is represented by the point O.
The forces acting on the lawn mover are (i) applied force F, (ii) weight of the mover W downward, (iii) force of friction acting opposite to the direction of motion, (iv) reaction of ground on the mover (R). 1 In case of pushing the mover, the horizontal component of push Fcos $\Teta $ in forward direction and vertical component Fsin $\Teta $ in downward direction. The total downward force = W + Fsin $\teta $