Equations of projectile motion

How can we simplify these equations of motion for projectiles? We use the fact that gravity accelerates down; therefore, ay = –g and ax = 0! The equations of motion simplify a great deal because all the terms that include ax become zero. Also, to make the math simpler, we choose the initial position to be zero, so x0 = 0 m and y0 = 0 m. Read the text aloud
Let’s first examine the motion in the x-direction. Since there is no acceleration in x, the component of velocity in the x-direction is constant. The projectile moves with constant velocity along x! The x position changes linearly, as shown in equation (6.6). Read the text aloud
(6.6) x= v x0 t v x = v x0
x  = position in x-direction (m)
vx0  = initial velocity in x-direction (m/s)
vx  = velocity component in x-direction (m/s)
t  = time (s)
Projectile motion
Now look at the equations of motion in the y-direction. The acceleration in y has a constant value of −g. As we learned in Chapter 4, constant (nonzero) acceleration results in velocity that changes linearly, as shown in equation (6.7). Position in the y-direction is a function of t and t2, as also shown in equation (6.7). Read the text aloud
(6.7) y= v y0 t 1 2 g t 2 v y = v y0 gt
y  = position in y-direction (m)
vy0  = initial velocity in y-direction (m/s)
vy  = velocity component in y-direction (m/s)
t  = time (s)
g  = acceleration due to gravity = 9.8 m/s2
Projectile motion
Equations (6.6) and (6.7) are the equations of projectile motion when gravity is acting in the negative y-direction. The initial velocity given to the projectile—soccer ball, cannonball, etc.—has components vx0 in the x-direction and vy0 in the y-direction. Read the text aloud
Projectile motion for a hit baseball
Consider a baseball player hitting a ball with an upward velocity of 30 m/s at an angle of 60°above horizontal. The ball’s initial velocity has components of 15 and 26 m/s in the x- and y-directions, respectively. Applying equations (6.6) and (6.7) predicts the trajectory illustrated above—with the magnitude of the velocity calculated from v2 = vx2 + vy2. Read the text aloud
In the illustration of the fly ball above, the position of the ball is depicted at fixed time intervals (every 0.5 s) to create a particle model of its motion. The ball positions are closest to each other at the top of the trajectory, which means that the speed is slowest there. The ball positions are furthest apart near the ground where the speed is fastest. Read the text aloud
When the baseball is first hit, its velocity has a position angle of 60° with the horizontal. After 2 s, what is the position angle of its velocity? Show

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