![]() ![]() At what direction should the banana be fired so that the monkey will catch it? The monkey release the branch when the banana is fired. The x component of the velocity remains constant at its initial value or vx=v0x The x component of the acceleration is ax=0 m/s2 Superposition principal We consider the horizontal and vertical parts of the motion separately In the horizontal or x direction, the moving object (the projectile) does not slow down in the absence of air resistance. Projectile motion has initial velocity Vo directed α above the horizon V0 α Projectile motion Projectile motion is a 2D motion of a free body – the only impact on the motion of free body is the acceleration due to gravity in downward direction. Find the spacecraft’s final velocity (magnitude and direction)? ![]() In the y direction, the analogous quantities are v0y= +14 m/s ay= +12 m/s2 At a time of t=7.0 s, find the x and y components of the spacecraft’s displacement?Ĭheck Equation Solution 1 The motion in the x direction and the motion in the y direction can be treated as a 1D motion subject to the equations of kinematics for constant accelerationĮxample 1 – cont. Engine parallel to YĮxample 1 In the +x direction, the spacecraft has:an initial velocity component of v0x= +22 m/s an acceleration component of ax= +24 m/s2. ![]() Similarly, the y part of the motion occurs exactly as it would if the x part of the motion did not exist In other words, the x and y motions are independent of each other. It is important to realize that: the x part of the motion occurs exactly as it would if the y part did not occur at all. A spacecraft equipped with two engines that are mounted perpendicular to each other Engine parallel to XĮquation of Kinematics in 2D – cont. Terms The average acceleration has the same direction as the change in velocity In the limit that the elapsed time becomes infinitesimally small, the average acceleration becomes equal to the instantaneous acceleration The acceleration has a vector component ax along the x direction and a vector component ay along the y directionĮquation of Kinematics in 2D Since displacement, velocity and acceleration are vectors, each have 2 components in 2D. The vector components Vx and Vy of the velocity, are parallel to the x and y axes The average acceleration is defined just as it is for 1D motion, as the change in velocity, divided by the elapsed time Terms – Average acceleration V is tangent to the path of the car. Terms – Average Velocity The average velocity of the car between two positions is defined in a manner similar to 1D motion The average velocity vector has the same direction as the displacement vector The average velocity v becomes equal to the instantaneous velocity in the limit that t becomes infinitesimally small ( t 0 s) Terms - Displacement The race car is at two different positions along the curve, r and r0 The displacement of the car is the vector drawn from the initial position r0 at time t0 to the final position r at time t The magnitude of r is the shortest distance between the two positions Displacement, Velocity and Acceleration ĭisplacement, Velocity and Acceleration 2D motion refers to situations in which the motion is along a curved path that lies in a plane Such motion can be described using the same concepts as used for 1D motion Due to the curved path, the location vector r at each point in time is pointing in different direction (and not parallel to line as in 1D).
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