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# 2DMotionb - Physics 201 Lecture 4 Today's lecture will be...

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3/27/08 Physics 201, UW-Madison 1 Physics 201: Physics 201: Lecture Lecture 4 4 Today’s lecture will be on More on 2D motion Addition of velocities

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3/27/08 Physics 201, UW-Madison 2 Question Question Can a vector have a component bigger than its magnitude? Yes No The square of magnitude of a vector R is given in terms of its components by R 2 = R x 2 + R y 2 Since the square is always positive the components cannot be larger than the magnitude
3/27/08 Physics 201, UW-Madison 3 Question Question The sum of the two components of a non-zero 2-D vector is zero. Which of these directions is the vector pointing in? 45 o 90 o 135 o 180 o The sum of components is zero implies R x = - R y The angle, θ = tan -1 ( R y / R x ) = tan -1 -1 = 135 o = -45 o (not unique, ± multiples of 2 π ) -45 o 135 o

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3/27/08 Physics 201, UW-Madison 4 Summary of Lecture Summary of Lecture 3 Kinematics in Two Dimensions Kinematics in Two Dimensions x = x 0 + v 0x t + 1/2 a x t 2 v x = v 0x + a x t v x 2 = v 0x 2 + 2a x Δ x y = y 0 + v 0y t + 1/2 a y t 2 v y = v 0y + a y t v y 2 = v 0y 2 + 2a y Δ y x, y and z motions are independent ! They share a common time t
3/27/08 Physics 201, UW-Madison 5 Without air resistance, an object dropped from a plane flying at constant speed in a straight line will 1. Quickly lag behind the plane. 2. Remain vertically under the plane. 3. Move ahead of the plane Question? Question? There is no acceleration along horizontal - object continues to travel at constant speed (same as that of the plane) along horizontal. Due to gravitational acceleration the object’s speed downwards increases.

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3/27/08 Physics 201, UW-Madison 6 You are a vet trying to shoot a tranquilizer dart into a monkey hanging from a branch in a distant tree. You know that the monkey is very nervous, and will let go of the branch and start to fall as soon as your gun goes off. On the other hand, you also know that the dart will not travel in a straight line, but rather in a parabolic path like any other projectile. In order to hit the monkey with the dart, where should you point the gun before shooting? 1 Right at the monkey
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2DMotionb - Physics 201 Lecture 4 Today's lecture will be...

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