Question

if a 200 m/s running car pushes me , then will i be thrown with the same 200 m/s speed or more or less. when will my speed be highest and lowest?? and will the speed decrease in respect of time ??

Answer 1

Answer on Question #48576 – Physics - Mechanics | Kinematics | Dynamics

if a $200\,\mathrm{m/s}$ running car pushes me, then will I be thrown with the same $200\,\mathrm{m/s}$ speed or more or less. When will my speed be highest and lowest?? and will the speed decrease in respect of time ??

Solution:

$M$ – mass of the car;

$m$ – mass of the person;

$$v_1 = 200\,\frac{m}{s} \text{ – initial velocity of the car};$$ $$u_1 = 0 \text{ – person's initial velocity};$$

$v_2$ – final velocity of the car;

$u_2$ – person's final velocity;

The law of conservation of momentum states that the total momentum of a closed system does not change. This means that when two objects collide the total momentum of the objects before the collision is the same as the total momentum of the objects after the collision.

$$M_{\text{before}} = M_{\text{after}} \quad (1)$$ $$M_{\text{before}} = M_{\text{car}_1} + M_{\text{person}_1} = M v_1 + m u_1 \quad (2)$$ $$M_{\text{after}} = M_{\text{car}_2} + M_{\text{person}_2} = M v_2 + m u_2 \quad (3)$$

(3) and (2) in (1):

$$M v_1 + m u_1 = M v_2 + m u_2$$

Because after pushing the person, we can assume that the person and the car will move as one system, thus they will move with the same velocity $u_2$:

$$v_2 = u_2$$ $$M v_1 + m u_1 = M u_2 + m u_2$$ $$M v_1 + m u_1 = u_2(M + m)$$ $$u_2 = \frac{M v_1 + m u_1}{M + m} = \frac{M \cdot 200\,\frac{m}{s} + m \cdot 0}{M + m} = 200\,\frac{m}{s} \left(\frac{M}{M + m}\right) = 200\,\frac{m}{s} \left(\frac{M}{M + m}\right)$$

Because of $\frac{M}{M + m}$ always is less than 1, final velocity of the person will be less than $200\,\frac{m}{s}$.

$$u_2 < 200\,\frac{m}{s}$$

The velocity of the person will be highest after end of the pushing (when it will be momentum $M_{\text{after}}$), the lowest velocity will be before pushing ($u_1 = 0$ when there is a momentum $M_{\text{before}}$)

The speed of the object will change in respect of time only if the momentum of the system will change (momentum will decrease – the speed will decrease; momentum will increase – the speed will increase)

Answer: final velocity of the person: $u_2 = 200\,\frac{m}{s} \left(\frac{M}{M + m}\right)$.

https://www.AssignmentExpert.com