El oído humano percibe sonidos cuyas frecuencias están comprendidas entre 20 y 20000 Hertz. Calcular la longitud de onda de los sonidos extremos, si el sonido se propaga en el aire con la velocidad de 330 ms.

The position of a dragonfly that is flying parallel to the ground is given as a function of time by r⃗ =[2.90m+(0.0900m/s2)t2]i^− (0.0150m/s3)t3j^. a: at what value of t does the velocity vector of the insect make an angle of 34.0 degree clockwise from the x-axis? b: at the time calculated in part (a), what is the magnitude of the acceleration vector of the insect? c : at the time calculated in part (a), what is the direction of the acceleration vector of the insect?

Aparticle of mass m is projected with an initial velocity v0 in a direction making an angle α with the horizontal level ground as shown in the figure. the motion of the particle occurs under a uniform gravitational field g pointing downward. (a) write down the lagrangian of the system by using the cartesian coordinates (x, y). (b) is there any cyclic coordinate(s). if so, interpret it (them) physically. (c) find the euler-lagrange equations. find at least one constant of motion. (d) solve the differential equation in part (c) and obtain x and y coordinates of the projectile as a function of time. (e) construct the hamiltonian of the system, h, and write down the hamilton’s equations (canonical equations) of motion.

Acoyote chasing a rabbit is moving 8.00 m/s due east at one moment and 8.80 m/s due south 4.25 s later. let the x axis point due east and the y axis point due north. find the direction of the coyote's average acceleration during that time.