This is a challenging problem. Solve it on paper, writing out each step carefully. When doing calculations, do not round intermediate values. Note: If you have approached the problem in a principled way, do not abandon your approach if your numerical answer is not accepted; check your calculations! Four protons (each with mass 1.7 × 10-27 kg and charge 1.6 × 10-19 C) are initially held at the corners of a square that is 5.0 × 10-9 m on a side. They are then released from rest. What is the speed of each proton when the protons are very far apart? (You may assume that the final speed of each proton is small compared to the speed of light.)

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.