Acurve ball is a type of pitch in which the baseball spins on its axis as it heads for home plate. if a curve ball is thrown at 35.6 m/s (80 mph ) with a spin rate of 29 rev/s , how many revolutions does it complete before reaching home plate? assume that home plate is 18.3 m (60 ft) from the pitching mound and that the baseball travels at a constant velocity.

Apulley with a mechanical advantage of 5 will require you to pull times the amount of rope. a. 1/5 b. 5 c. 10 d. 15

A1000-kg weather rocket is launched straight up. the rocket motor provides a constant acceleration for 16-s, then the motor stops. the rocket altitude 20-s after launch is 510-m. you can ignore any effects of air resistance. a. what was the rocket’s acceleration during the first 16-s? b. what is the rocket’s speed as it passes through a cloud 5100-m above the ground?

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.