Consider a child playing with a toy car of mass M. The car is moving with velocity v. A
stream of water is then shot towards the car. All the water shot at the car is captured and
stored in a small tanker at the back of the car at the rate dm/dt. The water has velocity
u before it hits, and comes to rest (with respect to the car) after hitting. What force must
the child apply to the car to keep it moving with velocity v?

Question

Consider a child playing with a toy car of mass M. The car is moving with velocity v. A
stream of water is then shot towards the car. All the water shot at the car is captured and
stored in a small tanker at the back of the car at the rate dm/dt. The water has velocity
u before it hits, and comes to rest (with respect to the car) after hitting. What force must
the child apply to the car to keep it moving with velocity v?

badhi · Answer

If we consider the water jet, it will be providing a constant amount of force against the direction of the moving vehicle. So if we find this force, we can see how much force we should apply to cancel this force from water enabling the vehicle to move at a constant velocity

you know that the definition of the Force is,
$$F= \frac{P_{t+\Delta t} -P_t}{\Delta t}$$

At this $\Delta t$ time, the $\Delta t \frac{dm}{dt}$ amount of water mass will change its velocity from u to 0 ( im not sure $u$ is wrt to the vehicle or ground ill take that is wrt to ground). So the vehicle sees that a water jet with $u+v$ hits the vehicle and comes to rest

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So i hope youll be able to find the momentums at $t$ and $t+\Delta t$  and from that find the force that is applied on the vehicle from the water jet :)