Two children who are both adept at physics by the same toy rocket from the store and wish to do the following. One child goes to the top of a small cliff and launches his rocket with initial speed v$0=23\mathrm{.}2$ m$/$sv$0=23\mathrm{.}2$ m$/$s at an angle of $=12\mathrm{.}0=12\mathrm{.}0$ upwards from the horizontal. Her friend, still at ground level, namely h$=8\mathrm{.}55$ mh$=8\mathrm{.}55$ m below the top of the cliff, walks out a distance dd and wishes to shoot her rocket straight up into the sky 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. How high $($from ground level, i$.$e$.,$ from where the rocket that was launched directly upwards took off$)$ do the two rockets collide?