Homework 3 Classical Mechanics (Phys701) Due: September 26, 2011 Problem 4-21 A particle is thrown up vertically with initial speed v0 , reaches a maximum height and falls back to ground. Show that the Coriolis deﬂection when it again reaches the ground is opposite in direction, and four times greater in magnitude, than the Coriolis deﬂection when it is dropped t rest from the same maximum height. Problem 4-22 A projectile is ﬁred horizontally along Earth’s surface. Show that to a ﬁrst approximation the angular deviation from the direction of the ﬁre resulting from the Coriolis eﬀect varies linearly with time at a rate ω cos θ where ω is the angular velocity of Earth’s rotation and θ is the co-latitude, the direction of deviation being to the right in the northern hemisphere. Problem 4-23 The Foucault pendulum experiment consists of setting a long pendulum in motion at a point on the surface of the rotating Earth with its momentum originally in the vertical plane containing
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