A frog is sitting on a lily pad when it sees a delicious fly. He darts out his tongue at a speed of 3.90 m/s to catch the fly. The tongue has a mass of 0.410 g, and the rest of the frog plus the lily pad have a mass of 12.5 g. What is the recoil speed of the frog and the lily pad? Ignore drag forces on the pad due to the water.

The mass of a muon is 207 times the electron mass; the average lifetime of muons at rest is 2.21 μs. in a certain experiment, muons moving through a laboratory are measured to have an average lifetime of 7.04 μs. for the moving muons, what are (a) β (b) k, and (c) p? the rest energy of the electron is 0.511 mev.

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 ⇒

Why is rain likely when warm, moisture-laden air meets cold air? a) the lighter warm air will rise and cool down, causing condensation and rain. b) the cold air moves faster and pushes the warm air away, causing condensation and rain. c) the moisture in the warm air condenses on contact with the cold air, causing rain to fall. d) the cold air mixes with the warm air, reducing its temperature causing moisture to condense.