Imagine that I have a ping-pong ball and a bowling ball resting on the floor of our classroom. I go up to the bowling ball and give it a push so that it starts rolling. If I give a push of the exact same strength to the ping-pong ball, how will the resulting motion of the ping-pong ball be different

the speed and aceleration of the ping pong ball is greater than that of the bowling ball.

Explanation:

We can analyze this exercise from several points of view, if we use Newton's second law

Bowling ball

           F = M a₁

pingpongg ball

           F = m a₂

as the forces the same

          M a₁ = m a₂

          a₂ = a₁

Since the mass of the bowling ball is much greater than the ping pong ball,

          a₂ »a₁

so the acceleration of the ping pong ball is much greater than the acceleration of the bowling ball.

If we use the relationship of momentum and momentum, assuming that the time for the two cases is the same and that both start from rest

Bowling ball

           I = F t = Δp

           I = M (v₁ - v₀)

Ping pong ball

           I = F t = Δp

           I = m (v₂ -v₀)

the impulse itself

          M v₁ = m v₂

          v₂ = v₁

so we conclude that the speed of the ping pong ball is much greater than the speed of the bowling ball.

In conclusion the speed and aceleration of the ping pong ball is greater than that of the bowling ball.

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.

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