How do you solve this physics problem ?

there are two A and B balls on a pool table at rest, one next to the other. After the impulse, the A-ball moves with an
acceleration of 12 m/s^2 and the B ball with an acceleration of 24 m/s^2. If the angle formed between the two balls is 60°, what will be the distance, in cm, between the two balls after one second, considering that neither of them has fallen into the hole?

THANK YOU

1 Answer
Jan 25, 2018

First we find the distance covered by each ball, then the distance between them. They are 2080 cm apart after 1 second.

Explanation:

For both balls, the initial velocity u=0 ms1, so:

s=ut+12at2

reduces to:

s=12at2

For Ball A:

s=121212=6 m

For Ball B:

s=122412=12 m

We can't simply subtract one from the other, though, because they are at a 60o angle to each other. We have a triangle with sides 6 and 12 m and a 60o angle between them. We can use the cosine law to find the third side of the triangle:

a2=b2+c22bccosA

=122+24221224cos60o

=144+5765760.5=432

Take the square root of both sides:

a=20.8 m

We were asked for the answer in cm, so it is 2080 cm.

(side note: this is clearly not a standard size pool or billiard table!)