What properties do all mechanical waves share?

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.

Currents in dc transmission lines can be 100 a or higher. some people are concerned that the electromagnetic fields from such lines near their homes could pose health dangers. for a line that has current 150 a and a height of 8.0 m above the ground, what magnetic field does the line produce at ground level? express your answer in teslas and as a percentage of the earth’s magnetic field, which is 0.50 g. is this value cause for worry?

Two masses are connected by a rope that hangs over a pulley as shown below. the pulley is a uniform cylinder of radius 푅=0.381meters and mass 푀=3.1푘푔. initially 푚"is on the ground and 푚#rests 2.5 meters above the ground. if the system is released, use conservation of energy to determine the speed of 푚#just before it strikes the ground. assume the pulley bearing is frictionless.