Astudent holds a diverging lens 25.0 cm from the lettering on a poster on the wall. a virtual image of the letters is formed 10.5 cm between the lens and the wall. what are the focal length of the lens and orientation of the image? a) 7.4 cm and upright b) 7.4 cm and inverted c) 18.1 em and upright d) 18.1 em and inverted e) -7.4 cm and upright

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.

Suppose a soccer ball is kicked from the ground at an angle 20.0º above the horizontal at 8.00 m/s. the y-velocity is determined to be 2.74 m/s. how long will the ball be in the air? assume the ball lands at the same height at which it was kicked.

When you hold a rectangular object, how does the area of the side that is resting on your hand affect the pressure and the force that the object exerts?