Let k>0 be a constant. Suppose that particles P1 and P2 are moving, with velocity functions given by v1 (t) and v2(t) respectively, and that v2(t) = v1(kt). For a given interval a, b, the average velocity of particle P1 on [a, b] is equal to the average velocity of P2 on some interval [c, d]. Find c and d in terms of a and b.

A drowsy cat is looking at a window from across the room, and sees a flowerpot that sail first up and then down past the window. The pot is in view for a total of 0.54 s, and the top-to-bottom height of the window is 1.86 m. How high above the window top does the flowerpot go?

A projectile is fired from ground level at time t=0, at an angle θ with respect to the horizontal. It has an initial speed v0. In this problem we are assuming that the ground is level. Find the time tH it takes the projectile to reach its maximum height H.  Find tR, the time at which the projectile hits the ground after having traveled through a horizontal distance R. Find H, the maximum height attained by the projectile. Find the total distance R (often called the range) traveled in the x direction; see the figure in the problem introduction.

Problem 1: A car is moving on a straight road in a fixed direction at a constant speed of v = 31 km/h with respect to the road. You wish to state the kinematic vectors of the motion of the car by using a Cartesian coordinate system whose positive x-axis is pointed in the direction of the motion of the car and the origin is fixed at some point on the road. Part (a) What is the expression for the velocity of the car, using the speed v and the unit vectors i, j, and k? Expression : V = Select from the variables below to write your expression. Note that all variables may not be required. B, y, 0, i, b, d, g, h, j, k, m, n, P,S, v Part (b) What is the x-component of the position vector, in units of kilometers, at time t = 0.095 hr? Numeric : A numeric value is expected and not an expression. x =

Problem 3:   Consider a projectile launched with an initially horizontal velocity of 19.7m from a cliff of height h=9.23m. It travels a horizontal distance, d, before striking the ground at an angle θ below the horizontal. Use the Cartesian coordinate system provided in the drawing with the origin at the base of the cliff. Assume that air resistance is negligible.    Part (a)  How much time elapses, in seconds, from the moment the projectile is launched until it strikes the ground?   Part (b)  What is the horizontal distance, in meters, traveled by the projectile?  Part (c)  What is the speed of the projectile, in meters per second, as it strikes the ground? Part (d)  What is the impact angle, in degrees below the horizontal, at which the projectile strikes the ground?