You are in a car going 45 m/s. If you suddenly decelerate at a rate of 10 m/s2, how long will it take you to come to a full stop

You are given a vector a = 125i and an unknown vector b that is perpendicular to a. the cross-product of these two vectors is a × b = 98k. what is the y-component of vector b?

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.

22. the top of a cliff is located a distance h above the ground. at a distance h/2 there is a branch that juts out from the side of the cliff, and on this branch a bird's nest is located. two children throw stones at the nest with the same initial speed, one stone straight downward from the top of the cliff and the other stone straight upward from the ground. in the absence of air resistance, which stone hits the nest in the least amount of time?