Chapter 3 Problem Solving Suggestions

¢ To find the components of a vector use 

        and

¢ Given the components, find the vector by using the Pythagorean theorem (for its magnitude) and the inverse tangent of the ratio

         of its y and x components (for its direction).

¢ To add two vectors by components

 

        Ø add the x components of the individual vectors to find the x component of the resultant vector.

        Ø add the y components of the individual vectors to find the y component of the resultant vector.

        Ø use the Pythagorean theorem to find the magnitude of the resultant

        Ø use the inverse tangent of the ratio of the x and y components of the resultant to find the direction of the resultant.

¢ Projectile Motion Problems

 

        Ø there is acceleration a_y = -g in the y direction (assuming y is positive up).

        Ø there is no acceleration in the x direction. Thus, v_x0 = v_x = v₀

        Ø for a horizontal launch, v_x0 = v₀ and v_y0 = 0

        Ø for a launch with an angle q, the initial x and y components of velocity are v_x0 = v₀cosq₀ and v_y0 =v₀sinq₀ 

        Ø at the maximum height, velocity is in the x direction. That is, v_y = 0

        Ø when a projectile reaches the ground, v_y = 0

        Ø use symmetry. For example, the time it takes to reach the maximum height is half the total time of flight