FE Mechanical Dynamics, Kinematics, and Vibrations Practice Problems

The current FE Mechanical specification assigns 10-15 of the 110 exam questions to Dynamics, Kinematics, and Vibrations. 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 end of a horizontal conveyor at 24 ft/s. The discharge point is 18 ft above the surface of the stockpile, and air resistance is negligible. The horizontal distance from the discharge point to the point of impact is most nearly:

(A)17.9 ft
(B)25.4 ft
(C)26.8 ft
(D)46.0 ft

Show worked solution

Answer: (B)

The 18 ft drop takes 1.06 s, and the constant 24 ft/s horizontal velocity carries the gravel about 25.4 ft in that time.

Horizontal and vertical motion are uncoupled, so the drop height alone fixes the time of flight.

18 = \frac{1}{2} (32.2) t^{2}

t = 1.057 s

Zero horizontal acceleration holds the discharge speed constant over that interval.

x = (24) (1.057) = 25.4 ft

FE Reference Handbook — Dynamics: Particle Kinematics, Projectile Motion

Why the other choices appear

(A)Uses h rather than 2h in the fall-time expression, giving t = sqrt(18/32.2) = 0.748 s and x = 17.9 ft.
(C)Omits the square root on the fall time, taking t = 2h/g = 1.118 s so that x = 26.8 ft.
(D)Applies the SI gravitational constant 9.81 to USCS data, giving t = sqrt(36/9.81) = 1.916 s and x = 46.0 ft.