Vector Composition & Decomposition Practice Problems

A trolley loaded with water bottles is pushed up an incline, making an angle of 15.0° above the horizontal. The force applied has a magnitude of 120 N and makes an angle of 15.0° counterclockwise with respect to the incline. Calculate the F_x (horizontal) and F_y (vertical) components of the applied force.

A ski jumper has an acceleration of magnitude 8.00 m/s² just before he leaves the ramp. The ramp makes an angle of 18.0° counterclockwise with respect to the horizontal. Calculate the a_x and a_y components of the skier's acceleration before he leaves the ramp.

A box is dragged on a ramp with a force of 8.0 N parallel to the surface. The ramp makes an angle θ above the horizontal.  The horizontal component of the force vector is 6.0 N. Calculate the vertical component of the force vector.

A car has a position vector of 3.0 m with a direction of 45° clockwise from the north. Determine the components of the position vector along the x and y axes in the normal and tilted coordinate systems shown below.

 Determine the components of the force F (25.0 N, north) along the x and y axes of the tilted coordinate system shown below.

Use the following component pairs to determine the magnitude and direction of vector given by: (a) M_x =  4.3  mm, M_y = -8.6 mm (b) N_X =  -4.5 m, N_y = -8.7 m

You are provided with two vectors D and E. Vector D lies in the first quadrant, with a length of 4.20 cm and 40.0 degrees above the x-axis. Vector E lies in the fourth quadrant, with a length of 2.40 cm and 40.0 degrees below the x-axis. Find the magnitude and direction of D - E  using components.

Sketch the acceleration vector (a) and calculate the a_x and a_y components of a cart pulled by a horse and accelerating at 2.00 m/s², 35.0° clockwise from the positive x-axis.