Question

A 2500 kg delivery truck contains 125 cavans of rice, each of mass 50 kg. It is moving at a speed of 5.0 m/s. How many cavans of rice must be unloaded at a nearby grocery so that the ruck can move at 9.0 m/s and yet maintain the same momentum?

Answer 1

Let's first find the initial momentum of the delivery truck:

$$p_i=(M+mN)v,$$ $$p_i=(2500\ kg+50\ kg\cdot 125)\cdot 5.0\ \dfrac{m}{s}=43750\ \dfrac{kgm}{s}.$$

As we know from the conditions of the question, $p_i=p_f=p$, so we can write:

$$p=(M+mN)v,$$ $$N=\dfrac{p-Mv}{mv},$$ $$N=\dfrac{43750\ \dfrac{kgm}{s}-2500\ kg\cdot 9\ \dfrac{m}{s}}{50\ kg\cdot 9\ \dfrac{m}{s}}=47\ cavans.$$

Therefore, $N_{unload}=125-47=78\ cavans$.

Answer:

$N_{unload}=78\ cavans$.