Kyle, a 95.0 kg 95.0 kg football player, leaps straight up into the air (with no horizontal velocity) to catch a pass. He catches the 0.430 kg 0.430 kg ball precisely at the peak of his jump, when he is 0.488 meters 0.488 meters off the ground. He hits the ground 0.0333 meters 0.0333 meters away from where he leapt. If the ball was moving horizontally when it was caught, how fast was the ball traveling?

Many machines- including inclined planes such as ramps- increase the strength of the force put into the machine but decrease the distance over which the force is applied.

Ahorizontal wire is tied to supports at each end and vibrates in its second-overtone standing wave. the tension in the wire is 5.00 n, and the node-to-node distance in the standing wave is 6.28 cm. (a) what is the length of the wire? (b) a point at an anti- node of the standing wave on the wire travels from its maximum upward displacement to its maximum downward displacement in 8.40 ms. what is the wire's mass?

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.