A bitter controversy has recently broken out between the residents of a new housing development in the foothills and the Town Council over the safety of a number of large rocks perched on the slope of a hill that ends with a cliff, down to a lake, on the opposite side of which is the housing development. At the heart of the dispute is the relationship between the height above the edge of the cliff at which the rocks are balanced ( y ) and the distance, horizontally from the base of the cliff, that the rocks will travel (d) should they rolldown the hill. One group of engineers has done a study and concluded thathisproportional tod2.
However, a second group repeated the study and concluded thathisproportional tod. If the first group is correct, all rocks would land in the lake. If the secondis correct, some could overshoot the lake and smash into the houses. Both groupsinvestigated the situation using apparatus consisting of a sloped ramp and a steel ball. Inboth cases, the steel ball was rolled down the slope from different heights, andhanddwere measured. The UCD Physics Department has been approached to resolve thecontroversy and now asks you to investigate the situation urgently with the sameapparatus. A full report is sought, detailing all aspects of the experiments, measurements, calculations, and graphs as well as your findings on who is right or wrong. In particular, paycareful attention to your graphs ofdandhcompared to your graphs ofd2andh, and howthese graphs were used to determine the proportionality, as we will be showing them toreporters at a press conference later this week.