# Physics C 2d

Physics C – Homework Two Dimensional Motion 1. A particle moves along the parabola with equation Y = ? x2 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. . Suppose, instead, that the particle moves along the same parabola with a velocity whose x-component is given by vx = C/(1+x? )? 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. 3. 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 resistance is negligible. Determine expressions for the following quantities in terms of M, X, D, h, and g. Note that these symbols do not include the spring constant. a. The time elapsed from the instant the block leaves the table to the instant it strikes the floor . The horizontal component of the velocity of the block just before it hits the floor c. The work done on the block by the spring d. The spring constant 4. A ball of mass 0. 5 kilogram, initially at rest, is kicked directly toward a fence from a point 32 meters away, as shown above. The velocity of the ball as it leaves the kicker’s foot is 20 meters per second at an angle of 37° above the horizontal. The top of the fence is 2. 5 meters high. The kicker’s foot is in contact with the ball for 0. 05 second.

The ball hits nothing while in flight and air resistance is negligible. a. Determine the magnitude of the average net force exerted on the ball during the kick. b. Determine the time it takes for the ball to reach the plane of the fence. c. Will the ball hit the fence? If so, how far below the top of the fence will it hit? If not, how far above the top of the fence will it pass? d. On the axes below, sketch the horizontal and vertical components of the velocity of the ball as functions of time until the ball reaches the plane of the fence. [pic]