Projectile Motion Concepts

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Questions and Answers

What is the initial vertical velocity of the ball?

-5 m/s

0 m/s (correct)

-10 m/s

20 m/s

What is the acceleration in the y direction as the ball falls?

9.8 m/s²

20 m/s²

-9.8 m/s² (correct)

0 m/s²

How long does it take for the ball to fall to the ground?

0.5 seconds

2 seconds

1 second (correct)

0 seconds

What is the final vertical velocity of the ball just before it strikes the ground?

-10 m/s Signup and view all the answers

Using the Pythagorean theorem, what is the resultant velocity of the ball just before it strikes the ground?

22.36 m/s Signup and view all the answers

Which formula is used to find the final velocity in the y direction?

vfy = viy + at Signup and view all the answers

What is the horizontal velocity of the ball?

20 m/s Signup and view all the answers

What is the horizontal acceleration of the ball?

0 m/s² Signup and view all the answers

What distinguishes a scalar quantity from a vector quantity?

A scalar quantity is just a number, while a vector quantity is a number with a direction. Signup and view all the answers

In projectile motion, which component of velocity remains constant?

The horizontal component remains constant while the vertical component changes. Signup and view all the answers

Which statement about the ideal path of a projectile is true?

Time of ascent equals time of descent. Signup and view all the answers

What mathematical principle is used to calculate the magnitude of the resultant vector from its components?

Pythagorean Theorem. Signup and view all the answers

In vector addition, which step should be taken first to find the resultant vector?

Sum up all vectors in the y-direction. Signup and view all the answers

What does a vector represent in the context of projectile motion?

A quantity with both magnitude and direction. Signup and view all the answers

Which component is affected by gravity during projectile motion?

Only the vertical component is affected. Signup and view all the answers

What is the acceleration due to gravity during free fall?

-9.81 m/s² Signup and view all the answers

What shape does the path of a projectile typically follow in ideal conditions?

A parabola. Signup and view all the answers

In projectile motion, how does velocity change in the x direction?

It remains constant. Signup and view all the answers

Using the equation for vertical motion, y = ½ at², what does 'a' represent?

The acceleration due to gravity. Signup and view all the answers

What is the initial vertical velocity (viy) of an object that is dropped?

0 m/s Signup and view all the answers

What does the term 'dy' represent in vertical motion equations?

The change in vertical position. Signup and view all the answers

If a projectile is launched at a horizontal distance of 20m and falls 5m vertically, how long is the ball in the air?

1 second Signup and view all the answers

Which equation can be used to determine the horizontal position of a projectile?

x = vt Signup and view all the answers

When a projectile is launched, how does its path compare to the ideal straight-line path without gravity?

It falls below the straight-line path due to gravity. Signup and view all the answers

Study Notes

Projectile Motion

Projectile motion is the motion of an object thrown or projected into the air, subject to only the force of gravity.
Scalars are just numbers, like weight.
Vectors have both magnitude and direction, like velocity.
A vector can be resolved into two components.
Component vectors form right angles to each other.
An example of a component is the vertical component of the velocity and horizontal component of the velocity.
Projectile motion follows a parabolic path.
The horizontal component of velocity stays constant.
The vertical component of velocity changes due to gravity's effect.
Ideal projectile paths (no air resistance) have equal time up and down, and equal velocities up and down.
The actual path of a projectile may be different due to the presence of air resistance.
To add vectors mathematically:
- Sum the x-direction vectors (Σx).
- Sum the y-direction vectors (Σy).
- Draw Σx and Σy vectors head-to-tail, including direction.
- Draw the resultant vector (from start to end).
- Use the Pythagorean theorem to find the resultant vector's size.
The Pythagorean theorem states: C² = A² + B². (C is the hypotenuse, A and B are legs).
Examples of projectiles include cannonballs, stones, and spacecraft in orbit.
All objects experience a downward acceleration due to gravity (g = -9.81 m/s²).
Horizontal motion is unaffected by gravity (constant horizontal velocity).
Vertical motion is affected by gravity. The formula for vertical displacement (y) is: y = 0.5 * a * t².
In the x-direction, gravity has no effect. The velocity is constant. Horizontal position can be found by x = vt.
In the y-direction, gravity pulls downward. The y-position is given by y = 0.5 * a * t².
The actual projectile path is the combination of the vertical and horizontal motions.
Projectile motion examples: monkey, ballistics, juggling, moon feather.
To find the time in the air, use the vertical displacement equation. Use the constant velocity equation to solve for velocity in another direction.
To find resultant velocity, use Pythagorean theorem and the equation for both x and y directions.

Equations

Horizontal (x):
- V_fx = d_x/t
- d_x = V_ix * t + 0.5 * a_x * t²
- V_fx² = V_ix² + 2 * a_x * d_x
Vertical (y):
- V_fy = V_iy + a_y * t
- d_y = V_iy * t + 0.5 * a_y * t²
- V_fy² = V_iy² + 2 * a_y * d_y

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Description

Test your understanding of projectile motion, including the differences between scalars and vectors, and how to resolve component vectors. This quiz covers the parabolic paths followed by projectiles and the effects of gravity and air resistance on motion in two dimensions.