In which state of matter do atoms only vibrate in place and do not freely move around?

Astudent throws a water balloon with speed v0 from a height h = 1.76 m at an angle θ = 21° above the horizontal toward a target on the ground. the target is located a horizontal distance d = 9.5 m from the student’s feet. assume that the balloon moves without air resistance. use a cartesian coordinate system with the origin at the balloon's initial position. (a) what is the position vector, rtarge t, that originates from the balloon's original position and terminates at the target? put this in terms of h and d, and represent it as a vector using i and j. (b) in terms of the variables in the problem, determine the time, t, after the launch it takes the balloon to reach the target. your answer should not include h. (c) create an expression for the balloon's vertical position as a function of time, y(t), in terms of t, vo, g, and θ. (d) determine the magnitude of the balloon's initial velocity, v0, in meters per second, by eliminating t from the previous two expressions.

Amichelson interferometer operating at a 600 nm wavelength has a 3.02-cm-long glass cell in one arm. to begin, the air is pumped out of the cell and mirror m2 is adjusted to produce a bright spot at the center of the interference pattern. then a valve is opened and air is slowly admitted into the cell. the index of refraction of air at 1.00 atm pressure is 1.00028.how many bright-dark-bright fringe shifts are observed as the cell fills with air?

Along wire carrying a 4.2 a current perpendicular to the xy-plane intersects the x-axis at x=−1.7cm. a second, parallel wire carrying a 3.0 a current intersects the x-axis at x=+1.7cm. part a at what point on the x-axis is the magnetic field zero if the two currents are in the same direction? express your answer to two significant figures and include the appropriate units.