You are driving at the speed of 27.7 m/s (61.9764 mph) when suddenly the car in front of you (previously traveling at the same speed) brakes and begins to slow down with the largest deceleration possible without skid- ding. considering an average human reaction, you press your brakes 0.507 s later. you also brake and decelerate as rapidly as possible without skidding. assume that the coefficient of static friction is 0.868 between both cars’ wheels and the road. the acceleration of gravity is 9.8 m/s2 . calculate the acceleration of the car in front of you when it brakes. answer in units of m/s2.

Asystematic approach to problem solving is called a (an)

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.

Write a polynomial function with the given zeros x= -1,0,2show your work