On level ground a shell is fired with an initial velocity of
at 60.0° above the horizontal and feels no appreciable air
resistance. (a) find the horizontal and vertical components of the
shell’s initial velocity. (b) how long does it take the shell to reach
its highest point? (c) find its maximum height above the ground.
(d) how far from its firing point does the shell land? (e) at its
highest point, find the horizontal and vertical components of its
acceleration and velocity.

Aspring with a mass of 2 kg has a damping constant 14 kg/s. a force of 3.6 n is required to keep the spring stretched 0.3 m beyond its natural length. the spring is stretched 0.6 m beyond its natural length and then released. find the position of the mass at any time t. (assume that movement to the right is the positive x-direction and the spring is attached to a wall at the left end.)

Which type of circuit is becoming more common in residential electrical design and construction? a. hazardous-area circuit b. three-phase circuit c. 480-volt circuit d. communication circuit

The frequency of vibrations of a vibrating violin string is given by f = 1 2l t ρ where l is the length of the string, t is its tension, and ρ is its linear density.† (a) find the rate of change of the frequency with respect to the following. (i) the length (when t and ρ are constant) (ii) the tension (when l and ρ are constant) (iii) the linear density (when l and t are constant) (b) the pitch of a note (how high or low the note sounds) is determined by the frequency f. (the higher the frequency, the higher the pitch.) use the signs of the derivatives in part (a) to determine what happens to the pitch of a note for the following. (i) when the effective length of a string is decreased by placing a finger on the string so a shorter portion of the string vibrates df dl 0 and l is ⇒ f is ⇒ (ii) when the tension is increased by turning a tuning peg df dt 0 and t is ⇒ f is ⇒ (iii) when the linear density is increased by switching to another string df dρ 0 and ρ is ⇒ f is ⇒