A high-powered rifle fires a bullet with a muzzle speed of 1.00 km/s. The gun is pointed horizontally at a large bull’s eye target—a set of concentric rings—200 m away.
(a) How far below the extended axis of the rifle barrel does a bullet hit the target? The rifle is equipped with a telescopic sight. It is “sighted in” by adjusting the axis of the telescope so that it points precisely at the location where the bullet hits the target at 200 m.
(b) Find the angle between the telescope axis and the rifle barrel axis.
When shooting at a target at a distance other than 200 m, the marksman uses the telescopic sight, placing its crosshairs to “aim high” or “aim low” to compensate for the different range. Should she aim high or low, and approximately how far from the bull’s eye, when the target is at a distance of
(c) 50.0 m, (d) 150 m, or
(e) 250 m? Note: The trajectory of the bullet is everywhere so nearly horizontal that it is a good approximation to model the bullet as fired horizontally in each case.
What if the target is uphill or downhill?
(f) Suppose the target is 200 m away, but the sight line to the target is above the horizontal by 30°. Should the marksman aim high, low, or right on?
(g) Suppose the target is downhill by 30°. Should the marksman aim high, low, or right on? Explain your answers.