A block is attached to a spring and rests on a horizontal, frictionless surface. The block is pulled to the right and released from rest when the clock starts counting and t = 0. The block oscillates back and forth about its equilibrium position, and the motion at any time is described by:x(t) = (3.5 cm)cos[(0.8 rad/s)t].What is the value of the t the second time the block goes through the equilibrium position?

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.