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

Answer:

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# #ms^-1#, so:

#s=ut+1/2at^2#

reduces to:

#s=1/2at^2#

For Ball A:

#s=1/2*12*1^2=6# #m#

For Ball B:

#s=1/2*24*1^2=12# #m#

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

#a^2=b^2+c^2-2bc cosA#

#=12^2+24^2-2*12*24*cos60^o#

#=144+576-576*0.5=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!)