Question 3 Road map: We obtain the velocity fastest (A)By Taking the derivative of a(t) (B)By Integrating a(t) (C)By integrating the accel as function of displacement (D)By computing the time to bottom, then computing the velocity.

Question 3 Road map: We obtain the velocity fastest (A)By Taking the derivative of a(t) (B)By Integrating a(t) (C)By integrating the accel as function of displacement (D)By computing the time to bottom, then computing the velocity.

Chapter 12-5 Curvilinear Motion X-Y Coordinates

Here is the solution in Mathcad

Example: Hit target at Position (360’, -80’)

Example: Hit target at Position (360, -80)

12.7 Normal and Tangential Coordinates u t : unit tangent to the path u n : unit normal to the path

Normal and Tangential Coordinates Velocity Page 53

Normal and Tangential Coordinates ‘e’ denotes unit vector (‘u’ in Hibbeler)

‘e’ denotes unit vector (‘u’ in Hibbeler)

12.8 Polar coordinates

Polar coordinates ‘e’ denotes unit vector (‘u’ in Hibbeler)

Polar coordinates ‘e’ denotes unit vector (‘u’ in Hibbeler)

12.8 Polar coordinates In a polar coordinate system, the velocity vector can be written as v = v r u r + v θ u θ = ru r +r  u . The term  is called A) transverse velocity. B) radial velocity. C) angular velocity. D) angular acceleration...

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12.10 Relative (Constrained) Motion v A is given as shown. Find v B Approach: Use rel. Velocity: v B = v A +v B/A (transl. + rot.)

Vectors and Geometry x y  t  r(t) 

Given: vectors A and B as shown. The RESULT vector is: (A) RESULT = A - B (B) RESULT = A + B (C) None of the above

Given: vectors A and B as shown. The RESULT vector is: (A) RESULT = A - B (B) RESULT = A + B (C) None of the above

Make a sketch: A V_rel v_Truck B The rel. velocity is: V_Car/Truck = v_Car -vTruck Relative (Constrained) Motion V_truck = 60 V_car = 65

Make a sketch: A V_river v_boat B The velocity is: (A)V_total = v+boat – v_river (B)V_total = v+boat + v_river Relative (Constrained) Motion

Make a sketch: A V_river v_boat B The velocity is: (A)V_total = v+boat – v_river (B)V_total = v+boat + v_river Relative (Constrained) Motion

Rel. Velocity example: Solution

Example Vector equation: Sailboat tacking at 50 deg. against Northern Wind (blue vector) We solve Graphically (Vector Addition)

Example Vector equation: Sailboat tacking at 50 deg. against Northern Wind An observer on land (fixed Cartesian Reference) sees V wind and v Boat. Land

Plane Vector Addition is two-dimensional Relative (Constrained) Motion vBvB vAvA v B/A

Example cont’d: Sailboat tacking against Northern Wind 2. Vector equation (1 scalar eqn. each in i- and j- direction). Solve using the given data (Vector Lengths and orientations) and Trigonometry i

Chapter Relative Motion

Vector Addition

Differentiating gives:

Exam 1 We will focus on Conceptual Solutions. Numbers are secondary. Train the General Method Topics: All covered sections of Chapter 12 Practice: Train yourself to solve all Problems in Chapter 12

Exam 1 Preparation: Start now! Cramming won’t work. Questions: Discuss with your peers. Ask me. The exam will MEASURE your knowledge and give you objective feedback.

Exam 1 Preparation: Practice: Step 1: Describe Problem Mathematically Step2: Calculus and Algebraic Equation Solving