Projectile Motion SPH 4 U Projectiles A projectile
- Slides: 44
Projectile Motion SPH 4 U
Projectiles A projectile is an object on which the only force acting is gravity. It is said to be “in free fall” even if part of its motion is upward.
Projectiles A projectile may also be travelling horizontally while falling if its initial (launch) velocity had a horizontal component.
Parametric Equations As the vertical motion is accelerated any horizontal motion is not accelerated, the components are calculated separately:
Parametric Equations As the vertical motion is accelerated any horizontal motion is not accelerated, the components are calculated separately: Vertical acceleration is –g. Horizontal acceleration is zero.
Parametric Equations As the vertical motion is accelerated any horizontal motion is not accelerated, the components are calculated separately:
Parametric Equations As the vertical motion is accelerated any horizontal motion is not accelerated, the components are calculated separately: Note that the variable common to both sets of equations is Dt.
The Parabola Note that the path (or “trajectory”) of a projectile will therefore be parabolic.
Example 1: The Cliff A ball is launched at 15. 0 m/s [right] from the top of a 15. 0 m tower. How far does the ball travel horizontally before it lands?
Example 1: The Cliff A ball is launched at 15. 0 m/s [right] from the top of a 15. 0 m tower. How far does the ball travel horizontally before it lands? First, find the time it takes the ball to fall 15. 0 m:
Example 1: The Cliff First, find the time it takes the ball to fall 15. 0 m:
Example 1: The Cliff First, find the time it takes the ball to fall 15. 0 m:
Example 1: The Cliff First, find the time it takes the ball to fall 15. 0 m:
Example 1: The Cliff First, find the time it takes the ball to fall 15. 0 m:
Example 1: The Cliff Now find the horizontal distance travelled in 1. 75 s:
Example 1: The Cliff Now find the horizontal distance travelled in 1. 75 s:
The Initial Velocity If the initial velocity is not parallel or perpendicular to the horizontal, it must be broken down into its horizontal and vertical components:
The Range A ball is launched from ground level with an initial velocity of v 1 at an angle q with the horizontal. How far does the ball travel horizontally before it lands?
The Range A ball is launched from ground level with an initial velocity of v 1 at an angle q with the horizontal. How far does the ball travel horizontally before it lands? Note that the answer to this question will not be a number but an algebraic expression.
The Range
The Range We can discard this solution.
The Range Substituting into the equation for horizontal distance:
The Range Substituting into the equation for horizontal distance:
The Range Substituting into the equation for horizontal distance: (by trig identities)
The Range The advantage of deriving a general expression instead of calculating a number is that you can see the relationships between the variables. Ex. So a projectile on the moon, with 1/6 the gravity, will travel 6 times further.
The Range The advantage of deriving a general expression instead of calculating a number is that you can see the relationships between the variables. Ex. So a projectile on the moon, with 1/6 the gravity, will travel 6 times further. If the launch velocity is doubled, the projectile will travel 4 times further.
The Range You can also find maxima and minima: Which launch angle will give you the maximum horizontal distance?
The Range You can also find maxima and minima: Which launch angle will give you the maximum horizontal distance? The maximum value of sin 2 q is 1.
The Range You can also find maxima and minima: Which launch angle will give you the maximum horizontal distance? The maximum value of sin 2 q is 1.
The Range However, the expression only applies to objects launched from ground level. It can not be applied in cases such as:
Example 2: Up Off the Cliff A ball is launched at 15. 0 m/s [37 o above the horizontal] from the top of a 15. 0 m tower. How far does the ball travel horizontally before it lands?
Example 2: Up Off the Cliff A ball is launched at 15. 0 m/s [37 o above the horizontal] from the top of a 15. 0 m tower. How far does the ball travel horizontally before it lands?
Example 2: Up Off the Cliff
Example 2: Up Off the Cliff
Example 2: Up Off the Cliff
Example 2: Up Off the Cliff
Example 2: Up Off the Cliff Note that the ball stayed in the air longer and travelled further when launched slightly above the horizontal.
Example 2: At the Bottom What was the ball’s impact velocity?
Example 2: At the Bottom What was the ball’s impact velocity? Note that it is not zero upon impact. It is only zero after impact, after the ground has exerted a normal force on it to stop it.
Example 2: At the Bottom What was the ball’s impact velocity? Note that we still need to find the time first.
Example 2: At the Bottom What was the ball’s impact velocity? 11. 98 m/s 19. 37 m/s
Example 2: At the Bottom What was the ball’s impact velocity? 11. 98 m/s 19. 37 m/s
Example 2: At the Bottom What was the ball’s impact velocity? 11. 98 m/s 19. 37 m/s
More Practice Textbook Questions • p. 46 #3, 5 • p. 50 #9, 10 Tomorrow: “Projectile Motion Lab”
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