Explain why
$(a)$ a horse cannot pull a cart and run in empty space,
$(b)$ passengers are thrown forward from their seats when a speeding bus stops suddenly,
$(c)$ it is easier to pull a lawn mower than to push it,
$(d)$ a cricketer moves his hands backwards while holding a catch.

(N/A) In order to pull a cart,a horse pushes the ground backward with some force. The ground in turn exerts an equal and opposite reaction force upon the feet of the horse. This reaction force causes the horse to move forward. An empty space is devoid of any such reaction force. Therefore,a horse cannot pull a cart and run in empty space.
$(b)$ When a speeding bus stops suddenly,the lower portion of a passenger's body,which is in contact with the seat,suddenly comes to rest. However,the upper portion tends to remain in motion (as per the first law of motion). As a result,the passenger's upper body is thrown forward in the direction in which the bus was moving.
$(c)$ While pulling a lawn mower,a force at an angle $\theta$ is applied on it. The vertical component of this applied force $(F \sin \theta)$ acts upward,which reduces the effective weight of the mower $(mg - F \sin \theta)$. On the other hand,while pushing a lawn mower,the vertical component of the applied force acts in the direction of the weight of the mower,increasing the effective weight $(mg + F \sin \theta)$. Since the effective weight is lesser in the first case,pulling the lawn mower is easier than pushing it.
$(d)$ According to Newton's second law of motion,$F = ma = m \frac{\Delta v}{\Delta t}$. The impact force $(F)$ is inversely proportional to the impact time $(\Delta t)$,i.e.,$F \propto \frac{1}{\Delta t}$. By moving his hands backward,a cricketer increases the time of impact $(\Delta t)$,which results in a decrease in the stopping force,thereby preventing the hands from getting hurt.