Question

1. There is a famous intersection in Kuala Lumpur, Malaysia, where thousands of vehicles pass each hour. A 750 kg Tesla Model S traveling south crashes into a 1250 kg Ford F-150 traveling east. What are the initial speeds of each vehicle before collision if they stick together after crashing into each other and move at an angle of 320 and a common velocity of 18 m/s.

Answer 1

Solution :

Let the positive $x-axis$ is along the East and the positive $y$ direction is along the north.

Given :

Mass of the Tesla car, $m_1$ = $750 \ kg$

Mass of the Ford car, $m_2 = 1250 \ kg$

Now let the initial velocity of Tesla car in the south direction be = $-v_1j$

The initial momentum of Tesla car, $p_1 = -750 \ v_1$

Let the initial velocity of Ford car in the east direction be = $v_2 \ i$

So the initial momentum of the Ford car is $p_2=1250\ v_2 \ i$

Therefore, the initial velocity of both the cars is $p_i = p_1+p_2$

                                                                  $=1250 \ v_2 \ i - 750\ v_1 \ j$

Now the final velocity of both the cars is $v = 18 \ m/s$

So the vector form is :

$v = 18\cos 32\ i-18 \sin 32 \ j$

  $= 15.26 \ i - 9.54 \ j$

Therefore the momentum after the accident is

$p_f=(m_1+m_2) \times v$

    $=(750+1250) \times (15.26 \ i - 9.54 \ j)$

    $= 30520\ i -19080\ j$

According to the law of conservation of momentum, we know

$p_i = p_f$

$1250 \ v_2 \ i - 750\ v_1 \ j$  $= 30520\ i -19080\ j$

$1250 \ v_2 = 30520$

$v_2=24.4 \ m/s$

From, $750\ v_1 = 19080$

We get, $v_1=25.4 \ m/s$

Therefore the speed of Tesla car before collision = 25.4 m/s

The speed of ford car before collision = 24.4 m/s