1. A dolphin jumps out of the water with an initial velocity of 20 feet per
second (assume its starting height is O feet). Use the vertical motion
model, h = -16t2 + vt + s, where v is the initial velocity in feet per
second and s is the height in feet, to calculate the amount of time the
dolphin is in the air before it hits the water again. Round your answer
to the nearest tenth if necessary.
Time in air: seconds

The slotted link is pinned at o, and as a result of rotation it drives the peg p along the horizontal guide. compute the magnitude of the velocity and acceleration of p along the horizontal guide. compute the magnitudes of the velocity and acceleration of p as a function of θ if θ=(3t) rad, where t is measured in seconds.

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.

The substances that are necessary for producing of certain hormones and that store and transport vitamins