Physic Labs

Problem 1

A projectile is launched from level ground at speed uu and angle α\alpha above horizontal; neglect air resistance. Find its range and the angle giving maximum range; gravity is gg. Treat the projectile as a point mass returning to its launch height; take vertical upward as positive and neglect drag. (a) Find the flight time and range RR. (b) For fixed uu, find the launch angle and maximum range. (c) Find the maximum height for a general launch angle. Express each answer in terms of the supplied parameters, using SI units for any numerical evaluation. State the assumptions used, check dimensions at each result, and compare with the governing law to catch a sign error or a missing condition.
R=uxtf=u2sin⁡(2α)gR=u_x t_f=\frac{u^2\sin(2\alpha)}{g}
problems.proof.analysis

Combine the preceding equations to eliminate an intermediate quantity and isolate the requested one. This also shows explicitly how the result depends on the supplied parameters.