If an object is thrown upward at 128 feet per second from a height of 76 feet, its height S after t seconds is given by the following equation. S(t) = 76 + 128t − 16t2 (a) What is the average velocity (in ft/sec) in the first 4 seconds after it is thrown? ft/sec (b) What is the average velocity (in ft/sec) in the next 4 seconds?

Apackage of supplies is dropped from a plane, and one second later a second package is dropped. neglecting air resistance, the relative velocity of the 1st package viewed from the second will 56) a) increase. b) be constant. c) be zero. d) depend upon their weight. e) decrease

Aball is thrown straight up into the air with a speed of 21 m/s. if the ball has a mass of 0.1 kg, how high does the ball go? acceleration due to gravity is g = 9.8 m/s^2. a. 22.5 m b. 20.0 m c. 25.0 m d. 17.5 m

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 ⇒