The discussion focuses on determining the range of a projectile launched from a slingshot, specifically examining how varying the initial velocity affects the range while keeping the launch angle constant. The range formula, given by R = (v² * sin 2θ) / g, establishes that the range is proportional to the square of the initial velocity. Participants clarify that the slope of the graph representing range versus initial velocity can be derived as R'(v) = (2v * sin 2θ) / g, providing a mathematical basis for understanding the relationship between these variables.
PREREQUISITESStudents, educators, and physics enthusiasts interested in understanding projectile motion, particularly in experimental setups involving slingshots and the mathematical relationships governing range and initial velocity.
Prateek Kumar Jain said:
What do you mean of the "gradient" of the graph? Your graph must mean the range ##R## versus the initial velocity ##v,## and in this single-variable function, the gradient is just the slope.James Adfey said:
ok yeah I just meant the slope when I said gradient, and was wondering if there were any graphs where the slope is equal to the range, but if not I will just do a graph that shows the range vs initial velocity,tommyxu3 said:
If you knew the result ##R=\frac{v^2\sin 2\theta}{g},## then you can easily get the slope ##R'(v)=\frac{2v\sin 2\theta}{g}## and can get what point meets your demand, which, however, the condition seems not meaningful... or?James Adfey said:
ok yeah that makes sense, thankstommyxu3 said: