926 is for reference Use the result 973 of Problem 926 to do

9.26 is for reference

Use the result (9.73) of Problem 9.26 to do the following: A naval gun shoots a shell at colatitude 0 in a direction that is a above the horizontal and due east, with muzzle speed v0. (a) Ignoring the earth\'s rotation (and air resistance), find how long (/) the shell would be in the air and how far away (R) it would land. If = 500 m/s and a = 20 degree , what are t and R? (b) A naval gunner spots an enemy ship due east at the range R of pan (a) and. forgetting about the Coriolis effect, aims his gun exactly as in part (a). Find by how far north or south, and in which direction, the shell will miss the target, in terms of 12, v0, or. 0. and g. (It will also miss in the cast-west direction but this is perhaps less critical.) If the incident occurs at latitude 50degree north (0 = 40degree), what is this distance? What if the latitude is 50degree south? This problem is a serious issue in long-range gunnery: In a battle near the Falkland Islands in World War I, the British navy consistently missed German ships by many tens of yards because they apparently forgot that the Coriolis effect in the southern hemisphere is opposite to that in the north. In Section 9.8. we used a method of successive approximations to find the orbit of an object that is dropped from rest, correct to first order in the earth\'s angular velocity Ohm. Show in the same way that if an object is thrown with initial velocity v_0 from a point O on the earth\'s surface at latitude 0, then to first order in ft its orbit is [First solve the equations of motion (9.53) in zeroth order, that is. ignoring ft entirely. Substitute your zeroth-order solution for i, y, and z into the right side of equations (9.53) and integrate to give the next approximation. Assume that u_0 is small enough that air resistance is negligible and that g is a constant throughout the flight.)

Solution

a) u = 500 m/s

Ux = 500 cos 20= 470 m/s

Uy = 500 sin 20= 171 m/s

Time of flight = 2 x 171/ 9.8 = 34.9 seconds

Distance = Ux x t =470 x 34.9 = 16.403 km