If a projectile is fired due east from a point on the surfaceof earth at a north

Question

If a projectile is fired due east from a point on the surfaceof earth at a northern latitude with a velocity of magnitudeV0 and at an angle of inclinationto the horizontal of, show that the lateral deflection when the projectilestrikes earth is                                               d = 4V03/g2 xsin x sin2 cos If a projectile is fired due east from a point on the surfaceof earth at a northern latitude with a velocity of magnitudeV0 and at an angle of inclinationto the horizontal of, show that the lateral deflection when the projectilestrikes earth is                                               d = 4V03/g2 xsin x sin2 cos

Explanation / Answer

Choosing an appropriate coordinate system for this situation,you can figure out that the lateral deflection of the projectile isin the x direction and that the acceleration is ax = x'' = 2zvy =2( sin )(V0 cos ) Integrating this expression twice and using the initialconditions x'(0) = 0 and x(0) = 0, we obtain d = x(t) = V0t2 cos sin --> Eq.(2) Now, we treat the z motion of the particle as if it wereundisturbed by the Coriolis force. In this approximation, wehave z(t) = V0t sin - (1/2)gt2 from which the time T of impact is obtained by setting z =0: T = (2V0 sin )/g Substituting this value for T into Eq. 2, we find the lateraldeflection at impact to be d = x(t) =(4V03/g2)*sin cos sin2 , which can also bewritten the way you have it. from which the time T of impact is obtained by setting z =0: T = (2V0 sin )/g Substituting this value for T into Eq. 2, we find the lateraldeflection at impact to be d = x(t) =(4V03/g2)*sin cos sin2 , which can also bewritten the way you have it.

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