Physic Labs

Problem 1

A particle of mass mm slides from rest without friction down a plane of length LL inclined at angle α\alpha, then leaves its edge and lands on a floor HH below the edge. With gravitational acceleration gg, find the sliding time, launch speed, and horizontal range from the edge. Model each stage with the appropriate conservation law or equation of motion; quantities stated as constant remain fixed during that stage. (a) Establish the governing physical relation for each stage. (b) Determine the requested observables from the stated initial conditions and constraints. (c) Check signs, dimensions, and the physical limiting behavior of the results.
problems.proof.stepOf
problems.proof.prevStepproblems.proof.nextStep
H=v0sin⁡α tf+12gtf2,R=v0cos⁡α tf,tf=−v0sin⁡α+v02sin⁡2α+2gHg\boxed{H=v_0\sin\alpha\,t_f+\frac12gt_f^2,\quad R=v_0\cos\alpha\,t_f,\quad t_f=\frac{-v_0\sin\alpha+\sqrt{v_0^2\sin^2\alpha+2gH}}{g}}
problems.proof.analysis

Apply the model consistently to each part, then check dimensions and physical limits.