6. A frictionless cart sits on a ramp that is tilted down at an angle of 30.0° from horizontal. The cart is released from rest, with an initial position of * = [0 m] + [0.500 mlj It rolls down the ramp (down and to the right) once it is released, and it's acceleration points down the ramp, parallel to the ramp, with a magnitude of 4.90 m/s². Use a coordinate system where up is +y and to the right is +x. a. What are the x- and y-components of the cart's initial velocity? b. What are the x- and y-components of the cart's acceleration? c. Use your answers to parts a and b to find the cart's position and velocity 1.50 seconds after it is released. Write your answers in unit vector notation.

The force F has a magnitude of 470 N. Express F as a vector in terms of the unit vectors i and j. Identify the x and y scalar components of F. Assume F = 470 N, 0 = 15% j) N Answers: F = i Fx= Fy || 10 F ·x i + i N Z Z N

In the product F  = qv(x) B, take q = 5,  v= 2.0i + 4.0j + 6.0k and F = −30.0i −60.0j + 50.0k What then is B in unit-vector notation if Bx =B y?

Some cats can be trained to jump from one location to another and perform other tricks. Kit the cat is going to jump through a hoop. He begins on a wicker cabinet at a height of 1.769 m above the floor and jumps through the center of a vertical hoop, reaching a peak height 3.135 m above the floor. (Assume the center of the hoop is at the peak height of the jump. Assume that +x axis is in the direction of the hoop from the cabinet and +y axis is up. Assume g = 9.81 m/s².) (a) With what initial velocity did Kit leave the cabinet if the hoop is at a horizontal distance of 1.570 m from the cabinet? (Express your answer in vector form. Give your answer to at least two decimal places for each vector component.) Vo m/s (b) If Kit lands on a bed at a horizontal distance of 3.584 m from the cabinet, how high above the ground is the bed? m Need Help? Read It