Problem 1

A small body is projected from level ground with initial speed

u

at angle

\theta

above the horizontal in a uniform gravitational field of magnitude

g

directed downward. Put the origin at launch, neglect air resistance and Earth curvature, and take

0<\theta<\pi/2

so the body rises and returns to its launch height. (a) Resolve the initial velocity and write the time-dependent motion. (b) Find the flight time

T

and maximum height

H

. (c) Derive horizontal range

R

and the angle that maximizes it for fixed

u

problems.proof.stepOf

problems.proof.prevStep problems.proof.nextStep

u_x=u\cos\theta,\quad u_y=u\sin\theta

problems.proof.analysis

Resolve the initial velocity into a constant horizontal component and an upward vertical component. The projectile returns to its launch height and experiences no drag.

problems.proof.pitfall. The time to the apex is only half the flight time; do not use it as the time at which the projectile returns to the ground.