The gravitron is a ride where people are spun around in an enclosed chamber. The First Law of Motion says that a person in the gravitron will tend to travel in a straight line unless something forces him to change direction. In this case, the wall of the room pushes in on the person, causing them to accelerate centripetally. If they spin fast enough, the maximum force of static friction between a person and the wall becomes large enough to hold them in place on the wall against gravity. Imagine a gravitron that spins around 0.44 times per second. People feel pressed against the wall 3 meters from the center of the chamber. How fast are people moving as the chamber turns

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.