Batman, whose mass is 122 kg, is holding on to the free end of a 6.89 m rope, the other end of which is fixed to a tree limb above. he is able to get the rope in motion as only batman knows how, eventually getting it to swing enough that he can reach a ledge when the rope makes a 77.8 ◦ angle with the vertical. the acceleration of gravity is 9.8 m/s 2 . how much work was done against the force of gravity in this maneuver? answer in units of j.

Astring that is fixed at both ends has a length of 1.05 m. when the string vibrates at a frequency of 91.0 hz, a standing wave with five loops is formed. (a) what is the wavelength of the waves that travel on the string? (b) what is the speed of the waves? (c) what is the fundamental frequency of the string?

You are driving directly behind a pickup truck, going at the same speed as the truck. a crate falls from the bed of the truck to the road. (a) will your car hit the crate before the crate hits the road if you neither brake nor swerve? (b) during the fall, is the horizontal speed of the crate more than, less than, or the same as that of the truck?

With the simplified model of the eye, what corrective lens (specified by focal length as measured in air) would be needed to enable a person underwater to focus an infinitely distant object? (be careful-the focal length of a lens underwater is not the same as in air! assume that the corrective lens has a refractive index of 1.62 and that the lens is used in eyeglasses, not goggles, so there is water on both sides of the lens. assume that the eyeglasses are 1.90