Two children buy the same toy rocket from the store. One child goes to the top of a small cliff and launches his rocket with initial speed v$0=12\mathrm{.}1$v$0=12\mathrm{.}1$m$/$s at an angle of $=0\mathrm{.}778=0\mathrm{.}778$ radians upwards from the horizontal. Her friend, still at ground level, namely h$=8\mathrm{.}77$mh$=8\mathrm{.}77$m below the top of the cliff, walks out a distance d and wishes to shoot her rocket up at angle $=1\mathrm{.}49=1\mathrm{.}49$ radians from the horizontal into the sky towards the cliff and intercept her friend's rocket. See the figure below. Given that both children have the same toy rockets, they both have the same initial speeds. The two rockets are launched at the same time. What is the distance dd from the cliff need to be in order to ensure that the two rockets really do collide?