You stand on a bridge above a river and drop a rock into the water below from a height of 25 m. (assume no air resistance)

a. what is the acceleration of the rock as it falls?

b. how long does it take to hit the water?

c. how much more time would it take if instead of dropping the rock straight down you threw horizontally with a speed of 20 m/s?

d. you throw another rock at an angle of 65 degrees above the horizontal with a speed of 20 m/s. what are the x- and y- components of the rock's speed?

e. how long does it take the rock to reach its maximum height?

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 ⇒

What are atoms of the same element with varying number of neutrons

Who was the first scientist to measure speed as distance over time?