An amusement park designer wants his swing to have a centripetal acceleration of 21 m/s2. If the velocity of the swing is 13 m/s, how long
should the chain on the swing be?
A. 8.5 m
B. 9.5 m
C. 9.0 m
D. 8.0 m

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.

What is the acceleration of a spaceship that is initially at rest and then speeds up to 220 m/s in 20 seconds

Students design a model roller-coaster track. they place a rubber ball at the highest point on the track and let it go. the ball rolls along the track pulled only by the force of gravity. eventually, it comes to a stop. which change to the design will result in the ball moving the greatest distance?