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0. Math Review31m
- Math Review
  31m
1. Intro to Physics Units1h 29m
2. 1D Motion / Kinematics3h 56m
3. Vectors2h 43m
4. 2D Kinematics1h 42m
5. Projectile Motion3h 6m
6. Intro to Forces (Dynamics)3h 22m
7. Friction, Inclines, Systems2h 44m
8. Centripetal Forces & Gravitation7h 26m
9. Work & Energy1h 59m
10. Conservation of Energy2h 54m
11. Momentum & Impulse3h 40m
12. Rotational Kinematics2h 59m
13. Rotational Inertia & Energy7h 4m
14. Torque & Rotational Dynamics2h 5m
15. Rotational Equilibrium3h 39m
16. Angular Momentum3h 6m
17. Periodic Motion2h 9m
18. Waves & Sound3h 40m
19. Fluid Mechanics4h 27m
20. Heat and Temperature3h 7m
21. Kinetic Theory of Ideal Gases1h 50m
22. The First Law of Thermodynamics1h 26m
23. The Second Law of Thermodynamics3h 11m
24. Electric Force & Field; Gauss' Law3h 42m
25. Electric Potential1h 51m
26. Capacitors & Dielectrics2h 2m
27. Resistors & DC Circuits3h 8m
28. Magnetic Fields and Forces2h 23m
29. Sources of Magnetic Field2h 30m
30. Induction and Inductance3h 38m
31. Alternating Current2h 37m
32. Electromagnetic Waves2h 14m
33. Geometric Optics2h 57m
34. Wave Optics1h 15m
35. Special Relativity2h 10m

5. Projectile Motion

Intro to Projectile Motion: Horizontal Launch

Physics

5. Projectile Motion

Intro to Projectile Motion: Horizontal Launch

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3:14 minutes

Problem 15b

Textbook Question

A rifle is aimed horizontally at a target 50 m away. The bullet hits the target 2.0 cm below the aim point. (b) What was the bullet's speed as it left the barrel?

Verified step by step guidance

Step 1: Identify the known values from the problem. The horizontal distance to the target is 50 m, the vertical displacement of the bullet is 2.0 cm (convert to meters: 0.020 m), and the acceleration due to gravity is approximately 9.8 m/s². The bullet's initial vertical velocity is 0 m/s since it is fired horizontally.

Step 2: Use the vertical motion equation to determine the time it took for the bullet to fall 2.0 cm. The equation for vertical displacement is:

y = \frac{1}{2} g t^{2}

, where

y

is the vertical displacement,

g

is the acceleration due to gravity, and

t

is the time. Rearrange the equation to solve for

t

t = \sqrt{\frac{2}{g} y}

Step 3: Substitute the known values into the rearranged equation to calculate the time of flight. Use

y = 0.020

m and

g = 9.8

m/s².

Step 4: Use the horizontal motion equation to find the bullet's speed. The equation for horizontal motion is:

x = v t

, where

x

is the horizontal distance,

v

is the horizontal velocity, and

t

is the time. Rearrange the equation to solve for

v

v = \frac{x}{t}

Step 5: Substitute the known values into the rearranged equation for horizontal velocity. Use

x = 50

m and the time calculated in Step 3 to find the bullet's speed as it left the barrel.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Projectile Motion

Projectile motion refers to the motion of an object that is launched into the air and is subject to gravitational forces. In this scenario, the bullet follows a parabolic trajectory due to gravity acting on it after being fired horizontally. Understanding the principles of projectile motion is essential to analyze how the bullet travels and falls below the aim point.

Kinematic Equations

Kinematic equations describe the motion of objects under constant acceleration. In this case, the vertical displacement of the bullet can be calculated using the equation for vertical motion, which relates distance, initial velocity, acceleration due to gravity, and time. These equations allow us to determine how long the bullet was in the air, which is crucial for finding its horizontal speed.

Horizontal Velocity

Horizontal velocity is the speed at which an object moves along the horizontal axis. For the bullet, this velocity remains constant since there are no horizontal forces acting on it after it leaves the barrel. By calculating the time the bullet is in the air and knowing the horizontal distance to the target, we can determine the bullet's speed as it left the barrel.

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