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Projectile Motion. Important points to consider: The most straight-forward technique of solving these problems is to separate motion occurring in the ‘x’ direction and motion occurring in the ‘y’ direction.

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Projectile motion
Projectile Motion

Important points to consider:

  • The most straight-forward technique of solving these problems is to separate motion occurring in the ‘x’ direction and motion occurring in the ‘y’ direction.

  • Because we are considering no air friction, the body experiences an acceleration of zero in the ‘x’ direction. Therefore, vx is constant.

  • Because we are considering no air friction, movement in the ‘y’ direction is the same as a freely falling body:


Projectile motion1
Projectile Motion

Important points to consider:

  • When finding travel time, remember that the projectile must travel up, stop, and travel back down. So, at the top of the path (maximum height) vy = 0.

  • It’s very important to realize that the travel time is equal for both the ‘y’ and ‘x’ directions.

  • Always draw a coordinate system and clearly mark values. This is an excellent use for subscripts.

  • In these free-fall problems, final velocity is not zero. vf is the velocity of the body just before reaching the end of the fall.


v0

+ y

v0 y

+ x

v0 x

  • The Problem:

  • A baseball is thrown with an initial velocity of 10 m/s at an angle 60 o above horizontal. Find the following values:

    • 1. maximum height

    • 2. travel time (time the ball is in the air)

    • 3. distance traveled in the horizontal direction


In the “y” direction, treat the ball as though it was thrown vertically upward at 8.7 m/s.

At the top

According to our coordinate system


0 thrown vertically upward at 8.7 m/s.

0

Find maximum height:


0 thrown vertically upward at 8.7 m/s.

Find the time the ball is in the air. This is the time for the ball to rise 3.9 m and return to y = 0.

Rise time:


Find fall time. Treat this as a freely-falling body, where: thrown vertically upward at 8.7 m/s.

At the top


0 thrown vertically upward at 8.7 m/s.

0

So, yes, in the absence of air, it takes the same time to rise as it does to fall.


Distance in x-dir. thrown vertically upward at 8.7 m/s.

Finally, let’s find the distance the ball will travel in the horizontal (x) direction.

Remember that

The ball leaves with vox = 5.0 m/s and continues at that constant velocity in the x-direction for 1.8 s. Acceleration in the x-direction is zero because there is no force to change the motion of the ball.


0 thrown vertically upward at 8.7 m/s.

0


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