AP Physics C: Mechanics 1.5 Motion in Two or Three Dimensions Questions

Analyse two- and three-dimensional motion by resolving vectors, treating components independently, and connecting trajectory geometry with timing, range, and speed.

Exam points

resolve vector initial conditions and apply independent component equations of motion
derive projectile time, range, height, speed, or direction from horizontal and vertical motion
compare trajectories under different launches, reference motion, gravity, or landing heights
construct or interpret component graphs and parametric equations for multidimensional motion
combine perpendicular acceleration components to determine a general planar trajectory

Covered syllabus points

1.5.A—Describe the motion of an object moving in two or three dimensions. TOPIC 1.5 Motion in Two or Three Dimensions…

[Maximum number: 2]

A block of mass m is placed on top of an ideal spring of spring constant k. The block is pushed against the spring, compressing the spring a distance $\Delta x$ . The block is released from rest, leaves the spring at the position shown in the figure, travels upward, and enters a track with a constant radius of curvature R that has negligible friction. The block enters the track at point A, maintains contact with the track, and exits horizontally at point B, a distance 3 R above the point the block was released. The block then falls to the ground and lands a horizontal distance D from the end of the track. Express all algebraic answers in terms of $m, k, \Delta x, R$ , and physical constants, as appropriate. The size of the block is much smaller than the radius of curvature of the track.

Calculate the distance D that the block travels.

For correctly relating the height of fall to the time of fall
$y=y_{0}+v_{o y} t+\frac{1}{2} a_{y} t^{2} \therefore H=0+0+\frac{1}{2} g t^{2} \therefore t=\sqrt{\frac{(2)(4 R)}{g}}=\sqrt{\frac{8 R}{g}}$

1 point

For correctly substituting into the equation for constant velocity consistent with part (b)(i)
$D=v_{x} t=\left(\sqrt{\frac{k}{m}(\Delta x)^{2}-6 g R}\right)\left(\sqrt{\frac{8 R}{g}}\right)$

1 point

Total for part (d)

2 points

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Covered syllabus points

Question 1