Problem 1E: Given the position function r of a moving object, explain how to find the velocity, speed, and... Problem 2E: What is the relationship between the position and velocity vectors for motion on a circle? Problem 3E: Write Newtons Second Law of Motion in vector form. Problem 4E: Write Newtons Second Law of Motion for three-dimensional motion with only the gravitational force... Problem 5E: Given the acceleration of an object and its initial velocity, how do you find the velocity of the... Problem 6E: Given the velocity of an object and its initial position, how do you find the position of the object... Problem 7E: Velocity and acceleration from position Consider the following position functions. a. Find the... Problem 8E: Velocity and acceleration from position Consider the following position functions. a. Find the... Problem 9E: Velocity and acceleration from position Consider the following position functions. a. Find the... Problem 10E: Velocity and acceleration from position Consider the following position functions. a. Find the... Problem 11E: Velocity and acceleration from position Consider the following position functions. a. Find the... Problem 12E: Velocity and acceleration from position Consider the following position functions. a. Find the... Problem 13E: Velocity and acceleration from position Consider the following position functions. a. Find the... Problem 14E: Velocity and acceleration from position Consider the following position functions. a. Find the... Problem 15E: Velocity and acceleration from position Consider the following position functions. a. Find the... Problem 16E: Velocity and acceleration from position Consider the following position functions. a. Find the... Problem 17E: Velocity and acceleration from position Consider the following position functions. a. Find the... Problem 18E: Velocity and acceleration from position Consider the following position functions. a. Find the... Problem 19E: Comparing trajectories Consider the following position functions r and R for two objects. a. Find... Problem 20E: Comparing trajectories Consider the following position functions r and R for two objects. a. Find... Problem 21E: Comparing trajectories Consider the following position functions r and R for two objects. a. Find... Problem 22E: Comparing trajectories Consider the following position functions r and R for two objects. a. Find... Problem 23E: Comparing trajectories Consider the following position functions r and R for two objects. a. Find... Problem 24E: Comparing trajectories Consider the following position functions r and R for two objects. a. Find... Problem 25E: Trajectories on circles and spheres Determine whether the following trajectories lie on a circle in... Problem 26E Problem 27E: Trajectories on circles and spheres Determine whether the following trajectories lie on a circle in... Problem 28E: Trajectories on circles and spheres Determine whether the following trajectories lie on a circle in... Problem 29E: Trajectories on circles and spheres Determine whether the following trajectories lie on a circle in... Problem 30E: Trajectories on circles and spheres Determine whether the following trajectories lie on a circle in... Problem 31E: Solving equations of motion Given an acceleration vector, initial velocity u0, v0, and initial... Problem 32E: Solving equations of motion Given an acceleration vector, initial velocity u0, v0, and initial... Problem 33E: Solving equations of motion Given an acceleration vector, initial velocity u0, v0, and initial... Problem 34E: Solving equations of motion Given an acceleration vector, initial velocity u0, v0, and initial... Problem 35E: Solving equations of motion Given an acceleration vector, initial velocity u0, v0, and initial... Problem 36E: Solving equations of motion Given an acceleration vector, initial velocity u0, v0, and initial... Problem 37E: Two-dimensional motion Consider the motion of the following objects. Assume the x-axis is... Problem 38E: Two-dimensional motion Consider the motion of the following objects. Assume the x-axis is... Problem 39E: Two-dimensional motion Consider the motion of the following objects. Assume the x-axis is... Problem 40E: Two-dimensional motion Consider the motion of the following objects. Assume the x-axis is... Problem 41E: Two-dimensional motion Consider the motion of the following objects. Assume the x-axis is... Problem 42E: Two-dimensional motion Consider the motion of the following objects. Assume the x-axis is... Problem 43E: Solving equations of motion Given an acceleration vector, initial velocity u0, v0, w0, and initial... Problem 44E: Solving equations of motion Given an acceleration vector, initial velocity u0, v0, w0, and initial... Problem 45E: Solving equations of motion Given an acceleration vector, initial velocity u0, v0, w0, and initial... Problem 46E Problem 47E: Three-dimensional motion Consider the motion of the following objects. Assume the x-axis points... Problem 48E: Three-dimensional motion Consider the motion of the following objects. Assume the x-axis points... Problem 49E: Three-dimensional motion Consider the motion of the following objects. Assume the x-axis points... Problem 50E: Three-dimensional motion Consider the motion of the following objects. Assume the x-axis points... Problem 51E: Three-dimensional motion Consider the motion of the following objects. Assume the x-axis points... Problem 52E Problem 53E Problem 54E: Trajectory properties Find the time of flight, range, and maximum height of the following... Problem 55E: Trajectory properties Find the time of flight, range, and maximum height of the following... Problem 56E: Trajectory properties Find the time of flight, range, and maximum height of the following... Problem 57E: Trajectory properties Find the time of flight, range, and maximum height of the following... Problem 58E: Motion on the moon The acceleration due to gravity on the moon is approximately g/6 (one-sixth its... Problem 59E: Firing angles A projectile is fired over horizontal ground from the origin with an initial speed of... Problem 60E Problem 61E: Nonuniform straight-line motion Consider the motion of an object given by the position function... Problem 62E: A race Two people travel from P(4, 0) to Q(4, 0) along the paths given by... Problem 63E: Circular motion Consider an object moving along the circular trajectory r(t) = A cos t, A sin t,... Problem 64E Problem 65E: A circular trajectory An object moves clockwise around a circle centered at the origin with radius 5... Problem 66E Problem 67E: Speed on an ellipse An object moves along an ellipse given by the function r(t) = a cos t, b sin t,... Problem 68E: Travel on a cycloid Consider an object moving on a cycloid with the position function r(t) = t sin... Problem 69E Problem 70E: Golf shot A golfer stands 390 ft (130 yd) horizontally from the hole and 40 ft below the hole (see... Problem 71E: Another golf shot A golfer stands 420 ft (140 yd) horizontally from the hole and 50 ft above the... Problem 72E Problem 73E: Initial velocity of a golf shot A golfer stands 420 ft horizontally from the hole and 50 ft above... Problem 74E: Ski jump The lip of a ski jump is 8 m above the outrun that is sloped at an angle of 30 to the... Problem 75E: Designing a baseball pitch A baseball leaves the hand of a pitcher 6 vertical feet above and 60... Problem 76E Problem 77E Problem 78E: Parabolic trajectories Show that the two-dimensional trajectory x(t) = u0 t + x0 and... Problem 79E: Tilted ellipse Consider the curve r(t) = cos t, sin t, c sin t, for 0 t 2, where c is a real... Problem 80E: Equal area property Consider the ellipse r(t) = a cos t, b sin t, for 0 t 2, where a and b are... Problem 81E: Another property of constant | r | motion Suppose an object moves on the surface of a sphere with... Problem 82E Problem 83E format_list_bulleted