Question

Two cars collide at an icy intersection and stick together afterward. The first car has a mass of 1150 kg and was approaching at 5.00 m/s due south. The second car has a mass of 750 kg and was approaching at 25.0 m/s due west.
Calculate the final velocity of the cars. (Note that since both cars have an initial velocity, you cannot use Equations 7.6a and b. You must look for other simplifying aspects.)
Magnitude (answer in m/s

Direction ° (counterclockwise from west is positive)

(b) How much kinetic energy is lost in the collision? (This energy goes into deformation of the cars.)

Answer 1

Answer:

a) v = 10.3 m/s at 17.1° south of west

b)ΔE = 147,964.5 J

Explanation:

Let us consider west as positive x-axis and the south as positive y-axis

Given

Mass of the first car $m_{1}$ = 1150 kg

Mass of the second car $m_{2}$ =750 kg

Speed of the first car $v_{1}$ = 5.00 m/s in y axis

Speed of the second car $v_{2}$ = 25.0 m/s in x axis

Solution

Since there are no external forces the momentum is conserved

in X-axis

$m_{1}\times0+m_{2} u_{2} =(m_{1}+m_{2})v_{x} \\v_{x} =\frac{m_{2} u_{2}}{m_{1}+m_{2}} \\v_{x} =\frac{750\times25}{1150+750}\\v_{x} =\frac{18750}{1900}\\v_{x} = 9.87 m/s$

in Y-Axis

$m_{1}u_{1}+m_{2} \times0} =(m_{1}+m_{2})v_{y} \\v_{y} =\frac{m_{1} u_{1}}{m_{1}+m_{2}} \\v_{y} =\frac{1150\times5}{1150+750}\\v_{y} =\frac{5750}{1900}\\v_{y} =3.03 m/s$

Final velocity

$v = \sqrt{v_{x} ^{2} +v_{y} ^{2} } \\v = \sqrt{9.87 ^{2} +3.03 ^{2} } \\v = 10.3 m/s$

Direction

$\theta = acrtan(\frac{v_{y} }{v_{x} } )\\\theta = acrtan(\frac{3.03 }{9.87 } )\\\theta = 17.1^{o}$

Energy Lost = Initial kinetic energy - final kinetic energy

$\Delta E = [\frac{1}{2}m_{1}u_{1}^2 +\frac{1}{2}m_{2}u_{2}^2 ] - \frac{1}{2}(m_{1}+m_{2})v^2\\\Delta E = [\frac{1}{2}\times1150\times5}^2 +\frac{1}{2}\times750 \times 25^2 ] - \frac{1}{2}(1150+750})10.3^2\\\Delta E = 147,964.5 J$

Answer 2

Force acting during collision is internal so momentum is conserve so (initial momentum = final momentum) in both directions Two cars collide at an icy intersection and stick together afterward. The first car has a mass of 1150 kg and was approaching at 5.00 m/s due south. The second car has a mass of 750 kg and was approaching at 25.0 m/s due west. Let Vx is and Vy are final velocities of car in +x and +y direction respectively. initial momentum in +ve x (east) direction = final momentum in +ve x direction (east)

- 750*25 + 1150*0 = (750+1150)
Vx initial momentum in +ve y (north) direction = final momentum in +ve y direction (north)

750*0 - 1150*5 = (750+1150)
Vy from here you can calculate Vx and Vy so final velocity V is


V=(√V2x+V2y) 

and angle make from +ve x axis is

θ=tan−1(VyVx)

kinetic energy loss in the collision = final KE - initial KE