Problem 1

A projectile is launched from level ground at speed

u

and angle

\alpha

above horizontal; neglect air resistance. Find its range and the angle giving maximum range; gravity is

g

. 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

R

. (b) For fixed

u

, 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.

problems.proof.stepOf

problems.proof.prevStep problems.proof.nextStep

R=\frac{u^2\sin(2\alpha)}{g},\quad R_{\max}=\frac{u^2}{g}

problems.proof.analysis

The final part requires an independent relation from kinematics, a constitutive law, or a boundary condition. It extends the solution to a quantity not fixed by the earlier equations.