Question

Two point particles A and B are placed in line on a frictionless horizontal plane. If particle A
(mass 1 kg) is moved with velocity 10 m/s towards stationary particle B (mass 2 kg) and after
collision the two move at an angle of 45º with the initial direction of motion, then find :




(a) Velocities of A and B just after collision.

(b) Coefficient of restitution.​

Answer 1

Answer:

Hey mate, here is your Answer:)

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Explanation:

The very first step to solve such problems is to find the line of impact which is along the direction of force applied by A on B, resulting the stationary particle of B, line of impact can be determined. It this case, the line of impact is along the direction of motion of B, i.e. 45 with the initial direction of motion of A.

a). Answer in photo no. 1:)

B). Answer in photo no. 2;)

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Answer 2

$\displaystyle\Huge \bf\red{\underline{\underline{ANSWER}}} </p><p>$

Let the speed of the train be x km/hr and the speed of the bus is y km/hr.

So according to question and using

$\huge \boxed{\sf{Time = \frac{Distance}{speed}}} </p><p>$

Total distance =300 km

Mansi travels 60 km by train and 300−60=240 by bus in 4 minute,

$\bf\frac{60}{x} + \frac{240}{y} = \red4</p><p>$

and 100 km by train, 300−100=200 by bus, and takes 10 minutes more,

$\bf {\frac{100}{x} + \frac{200}{y} = 4 + \frac{1}{6} = \frac{24 + 1 }{6} = \purple{\frac{25}{6}}}</p><p>$

Now, let

$\bf\color{blue}{\frac{1}{x} = a}$

and.

$\bf \color{blue}{ \frac{1}{y} = b }$

$\bfthen 60a+240b=4.............(1)$

$\bf100a+200b=25/6----(2)$

multiply (1) by 5 and (2) by 6 we get

$\bf300a+1200b=20..........(3)$

$\bf600a+1200b=25...........(4)$

Subtracting (3) and (4) we get

$\bf \green{−300a=−5}$

$\bf{a = \frac{1}{60}}$

Putting the value of a in (1) we get

$\bf{60 \times \frac{1}{60} + 240b = 4}$

$</p><p> \bf240b = 3 \\ \\ \bf b = \frac{1}{80}$

Now ,

$\bf\frac{1}{x} = a \\ \\ \bf \red{a = 60 km/h \: \blue \bigstar}$

$\bf\frac{1}{y} = b \\ \\ \bf \red {b = 80 km/h \: \pink \bigstar}$

Hence, the speed of the train is 60 km/hr and the speed of the bus is 80 km/hr.