A projectile is fired with speed v0 at an angle from the horizontal as shown in the figure.
What is the highest point in the trajectory H in terms of acceleration due to gravity g, velocity v0, and angle θ? What is the range of the projectile R in terms of acceleration due to gravity g, velocity v0, and angle θ?
An artillery officer has the following problem. From his current position, he must shoot over a hill of height H at a target on the other side, which has the same elevation as his gun. He knows from his accurate map both the bearing and the distance R to the target and also that the hill is halfway to the target. To shoot as accurately as possible, he wants the projectile to just barely pass above the hill.
What is the angle in terms of H and R? What is the initial speed v0 in terms of g, R, and H? What is the flight time t of the projectile?
