Two Dimensional Motion
1. A particle moves along the parabola with equation Y = ½x2 shown below.
a. Suppose the particle moves so that the x-component of its velocity has the constant value vx = C; that is, x = Ct i. On the diagram above, indicate the directions of the particle's velocity vector v and acceleration vector a at point R, and label each vector. ii. Determine the y-component of the particle's velocity as a function of x. iii. Determine the y-component of the particle's acceleration.
b. Suppose, instead, that the particle moves along the same parabola with a velocity whose x-component is given by vx = C/(1+x²)½ i. Show that the particle's speed is constant in this case. ii.On the diagram below, indicate the directions of the particle's velocity vector v and acceleration vector a at point S, and label each vector. State the reasons for your choices. 2.
A ball of mass m is released from rest at a distance h above a frictionless plane inclined at an angle of 45° to the horizontal as shown above. The ball bounces elastically off the plane at point P1 and strikes the plane again at point P2. In terms of g and h determine each of the following quantities:
a.The velocity (a vector) of the ball just after it first bounces off the plane at P1.
b. The time the ball is in flight between points P1 and P2.
c.The distance L along the plane from P1 to P2.
d.The speed of the ball just before it strikes the plane at P2.
One end of a spring is attached to a solid wall while the other end just reaches to the edge of a horizontal, frictionless tabletop, which is a distance h above the floor. A block of mass M is placed against the end of the spring and pushed toward the wall until the spring has been compressed a distance X, as shown above. The block is released, follows the trajectory shown, and strikes the floor a horizontal distance D from the edge of the table. Air...