A 3kg ball moving at 8 m/s strikes a 2kg ball at rest, if the collision is elastic, what is the speed of the lighter ball if the heavier ball moves at 2m/s in the opposite direction

Speed of lighter ball is 4 m/s.

Explanation:

Applying the principle of conservation of linear momentum,

momentum before collision = momentum after collision.

+ = -

= 3 kg, = 8 m/s, = 2 kg, = 0 m/s ( since it is at rest), = 2 m/s, = ?

(3 x 8) + (2 x 0) = (8 x 2) - (2 x )

24 + 0 = 16 - 2

2 = 16 - 24

2 = -8

=

   = -4 m/s

This implies that the light ball moves at the speed of 4 m/s in the opposite direction of the heavier ball after collision.

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

according to question, we have said that if the population has twice its initial population, then it becomes

so, time taken to reach this above mentioned population is given by

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.