If a car takes a banked curve at less than a given speed, friction is needed to keep it from sliding toward the inside of the curve (a real problem on icy mountain roads). (a) calculate the minimum speed, in meters per second, required to take a 84 m radius curve banked at 16° so that you don't slide inwards, assuming there is no friction. (b) what is the minimum coefficient of friction needed for a frightened driver to take the same curve at 16 km/h?

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.