A Man Running to Catch a Bus A man is running at speed (much less than the speed of light) to catch a bus already at a stop. At , when he is a distance from the door to the bus, the bus starts moving with the positive acceleration .Use a coordinate system with at the door of the stopped bus. Exercise 2.34 A subway train starts from rest at a station and accelerates at a rate of for 14.0 . It runs at constant speed for 70.0 and slows down at a rate of until it stops at the next station. Tossing Balls off a Cliff Learning Goal: To clarify the distinction between speed and velocity, and to review qualitatively one-dimensional kinematics. A woman stands at the edge of a cliff, holding one ball in each hand. At time , she throws one ball straight up with speed and the other straight down, also with speed . For the following questions neglect air resistance. Pay particular attention to whether the answer involves "absolute" quantities that have only magnitude (e.g., speed) or quantities that can have either sign (e.g., velocity). Take upward to be the positive direction. Multiple Choice Question - 2.14 Short Answer Question - 2.2 Problem 2.85: Juggling Act A juggler performs in a room whose ceiling is a height 3.3 above the level of his hands. He throws a ball upward so that it just reaches the ceiling. Position, Velocity, and Acceleration Learning Goal: To identify situations when position, velocity, and /or acceleration change, realizing that change can be in direction or magnitude. If an object's position is described by a function of time, (measured from a nonaccelerating reference frame), then the object's velocity is described by the time derivative of the position, , and the object's acceleration is described by the time derivative of the velocity, . It is often convenient to discuss the average of the latter two quantities between times and : and . Introduction to Projectile Motion Learning Goal: To understand the basic concepts of projectile motion. Projectile motion may seem rather complex at first. However, by breaking it down into components, you will find that it is really no different than the one-dimensional motions that you have already studied. One of the most often used techniques in physics is to divide two- and three-dimensional quantities into components. For instance, in projectile motion, a particle has some initial velocity . In general, this velocity can point in any direction on the xy plane and can have any magnitude. To make a problem more managable, it is common to break up such a quantity into its x component and its y component . Consider a particle with initial velocity that has magnitude 12.0 and is directed 60.0 above the negative x axis. Breaking up the velocities into components is particularly useful when the components do not affect each other. Eventually, you will learn about situations in which the components of velocity do affect one another, but for now you will only be looking at problems where they do not. So, if there is acceleration in the x direction but not in the y direction, then the x component of the velocity will change, but the y component of the velocity will not. Now, consider this applet. Two balls are simultaneously dropped from a height of 5.0 . Projectile Motion Tutorial Learning Goal: Understand how to apply the equations for 1-dimensional motion to the y and x directions separately in order to derive standard formulae for the range and height of a projectile. A projectile is fired from ground level at time , at an angle with respect to the horizontal. It has an initial speed . In this problem we are assuming that the ground is level. Graphing Projectile Motion For the motion diagram given , sketch the shape of the corresponding motion graphs in Parts A to D. Use the indicated coordinate system. One unit of time elapses between consecutive dots in the motion diagram. Exercise 3.21: Win the Prize In a carnival booth, you win a stuffed giraffe if you toss a quarter into a small dish. The dish is on a shelf above the point where the quarter leaves your hand and is a horizontal distance of 2.1 from this point (the figure ). If you toss the coin with a velocity of 6.4 at an angle of 60 above the horizontal, the coin lands in the dish. You can ignore air resistance.