2004

1 (a).  A ball is thrown vertically upwards with an initial velocity of 20 m/s.
Once second later, another ball is thrown vertically upwards from the same point with an initial velocity of u m/s.
The balls collide after a further 2 seconds.

                (i).                  Show that u = 17.75.

              (ii).                  Find the distance traveled by each ball before the collision, giving your answers correct to the nearest metre.

ANSWER

The two balls collide 3 seconds after the first ball is thrown.

It is necessary to find out whether the first ball is still rising or is in fact falling when they collide.

The first ball reaches its maximum height when its speed is zero.

   No “s”     i.e.    i.e. t = 2.04 seconds

So the first ball is on the way down again when the two collide.

We can find the magnitude of its displacement, which will be less than the total distance travelled, by using vectors. Take the ground as zero, up as positive and down as negative.

   No “v”  = 15.9 m

The second ball travels this distance in 2 seconds.

  No “v”   i.e.   i.e. u =17.75.

1 (a) (ii)

The second ball travels a distance of 15.9 m as seen in part (i).

We need to find the maximum height of the first ball
then the distance it travels on the way back down.

Its maximum height is:

 

On the way down it travels

Thus the first ball travels a total distance of 20.4+4.5 = 24.9 m