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alekssr [168]
3 years ago
5

A 1445-kg car,c, moving east at 21.2m/s, collides with a 2625-kg car,d,moving south at 17.5 m/s, and the cars stick together. In

what direction and with what speed do they move after the collision
Physics
1 answer:
Vitek1552 [10]3 years ago
6 0

Answer:

<em>After the collision, they move with a speed of 13.57 m/s at 56.30° south of east</em>

Explanation:

<u>Conservation Of Momentum </u>

The total momentum of a system of particles with masses m1,m2,...mn that interact without the action of external forces, is conserved. It means that, being \vec P and \vec P' the initial  and final momentums respectively:

\vec P = \vec P'

Or equivalently, for a two-mass system

m_1\vec v_1+m_2\vec v_2=m_1\vec v_1'+m_2\vec v_2'

All the velocities are vectors. Let's express the velocities in magnitude v and direction \theta as (v,\theta). It's rectangular components will be

v_x=vcos\theta

v_y=vsin\theta

The first car is moving east at 21.2 m/s. Its velocity is

\vec v_1=(21.2,0^o)

Recall that East is the zero-degree reference for angles

Expressing in rectangular form:

\vec v_1==

The second car is moving south at 17.5 m/s. Its velocity is

\vec v_2=(17.5,270^o)

\vec v_2==

The total initial momentum is

\vec P=m_1\vec v_1+m_2\vec v_2

\vec P=1445+2625

\vec P=\ Kg.m/s

They collide and stick together in a common mass and velocity \vec v', thus

\vec P'=(m_1+m_2)\vec v'

It must be equal to the initial momentum, thus

(m_1+m_2)\vec v'=\ Kg.m/s

Solving for \vec v'

\displaystyle \vec v'=\frac{\ Kg.m/s}{m_1+m_2}

\displaystyle \vec v'=\frac{\ Kg.m/s}{4070}

\displaystyle \vec v'=\ m/s

The magnitude of \vec v' is

|\vec v'|=\sqrt{7.53^2+(-11.29)^2}=13.57\ m/s

The direction angle is

\displaystyle tan\theta=\frac{-11.29}{7.53}

\displaystyle \theta=-56.30^o

After the collision, they move with a speed of 13.57 m/s at 56.30° south of east

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