FE Other Disciplines Dynamics Practice Problems

The current FE Other Disciplines specification assigns 9-14 of the 110 exam questions to Dynamics. Form A contains 10 original problems in this area. The sample below is published in full, with the same worked-solution format used throughout the book.

Gravel leaves the head pulley of a conveyor horizontally at 4.2 m/s and falls freely 3.6 m to the surface of a stockpile. Air resistance is negligible. The horizontal distance from the discharge point to the point of impact is most nearly:

(A)2.54 m
(B)3.08 m
(C)3.60 m
(D)5.09 m

Show worked solution

Answer: (C)

A 0.857 s fall paired with an unchanged 4.2 m/s horizontal velocity puts the impact point 3.60 m from the discharge point.

Vertical motion is free fall from rest, so the drop height alone fixes the flight time.

t = \frac{2 h}{g} = \frac{2 ( 3.6 m )}{9.81 m/s ^{2}} = 0.857 s

Horizontal velocity is constant because no horizontal force acts during flight.

x = v_{0} t = (4.2 m/s) (0.857 s) = 3.60 m

FE Reference Handbook — Dynamics: Particle Kinematics, Projectile Motion

Why the other choices appear

(A)Omits the factor 2 inside the radical, using t = sqrt(h/g) = 0.606 s, which gives 4.2(0.606) = 2.54 m.
(B)Solves h = gt^2/2 incorrectly as t = 2h/g = 0.734 s, giving 4.2(0.734) = 3.08 m.
(D)Reports the straight-line distance from discharge point to impact point, sqrt(3.60^2 + 3.60^2) = 5.09 m, instead of the horizontal distance.