## Projectile Motion

4.3 Projectile Motion

### Learning Objectives

By the end of this section, you will be able to:

- Use one-dimensional motion in perpendicular directions to analyze projectile motion.
- Calculate the range, time of flight, and maximum height of a projectile that is launched and impacts a flat, horizontal surface.
- Find the time of flight and impact velocity of a projectile that lands at a different height from that of launch.
- Calculate the trajectory of a projectile.

Pause and Predict 4.3.1 |
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If v_{0} = 20 m/s and θ_{0} = 50°, at what time after the initial toss will the ball reach the apex of the trajectory? |

(a) 1.6 s |

(b) 1.8 s |

(c) 2.0 s |

(d) 2.3 s |

(e) 2.5 s |

Pause and Predict 4.3.2 |
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If v_{0} = 20 m/s and θ_{0} = 50° and the basket is 30 m away from you along the x-direction, how long will it take for the ball to land in the basket? |

(a) 1.5 s |

(b) 1.8 s |

(c) 2.0 s |

(d) 2.3 s |

(e) 2.5 s |

**Practice!**

Practice 4.3.1 |
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If you increase the initial vertical velocity of a projectile what happens to its horizontal velocity? |

(a) The horizontal velocity must increase if the initial vertical velocity increases. |

(b) The horizontal velocity won’t necessarily be affected if the initial vertical velocity increases. |

(c) The horizontal velocity must decrease if the initial vertical velocity increases. |

(d) The horizontal velocity must stay the same if the initial vertical velocity increases. |

Practice 4.3.2 |
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The horizontal component of the velocity of an object experiencing projectile motion ______. |

(a) decreases as it moves upward and increases as it moves downward. |

(b) stays constant the entire time it is in flight. |

(c) increases as it moves upward and decreases as it moves downward. |

(d) decreases the entire time it is in flight. |

(e) increases the entire time it is in flight. |

Practice 4.3.3 |
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In the figure, a basketball is moving in projectile motion. What can you say about the ball’s velocity at the top of its trajectory? |

(a) The velocity at the top is equal to the initial velocity. |

(b) The velocity at the top is equal to the y-component of the initial velocity. |

(c) The velocity at the top is equal to the x-component of the initial velocity. |

(d) The velocity at the top is equal to zero. |

Practice 4.3.4 |
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In an airless test-facility, a bullet is fired from a gun horizontally, at a height of 1 m. At the same time, another identical bullet is dropped from the same height. What is true about the acceleration of the two bullets while they are in flight? |

(a) The bullet fired from the gun has a smaller acceleration than the dropped bullet while they are in flight. |

(b) The bullet fired from the gun has a larger acceleration than the dropped bullet while they are in flight. |

(c) The bullet fired from the gun and the dropped bullet have the same acceleration while they are in flight. |

(d) The bullet fired from the gun may have a larger or smaller acceleration than the dropped bullet, depending on how fast it is fired from the gun. |

Practice 4.3.5 |
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A bullet is fired from a gun horizontally, at a height of 1 m. At the same time, another identical bullet is dropped from the same height. What is true about the impact velocities (or final velocities) of these two bullets? |

(a) The bullet fired from the gun will have the same non-zero impact velocity as the dropped bullet. |

(b) The bullet fired from the gun will have a smaller impact velocity than the dropped bullet. |

(c) The bullet fired from the gun will have the same impact velocity as the dropped bullet, which will be a velocity of zero. |

(d) The bullet fired from the gun will have a greater impact velocity than the dropped bullet. |

Practice 4.3.6 |
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During soccer practice, Maya kicked a soccer ball 37° off the ground at 25 m/s. What was the ball’s speed 2.2 s after she kicked it? |

(a) 26 m/s |

(b) 13 m/s |

(c) 21 m/s |

(d) 20 m/s |

Practice 4.3.7 |
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During soccer practice, Maya kicked a soccer ball 37° off the ground at 25 m/s. At t = 2.2 s after she kicked the ball, was it moving upward in its trajectory, downward in its trajectory, or was it at the apex of its trajectory? |

(a) Upward |

(b) Downward |

(c) At the apex |

Practice 4.3.8 |
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During soccer practice, Maya kicked a soccer ball 37° off the ground at 25 m/s. Max, the goalie, caught the ball 60 m away from Maya and 1.0 m off the ground. Max caught the ball ______ seconds after Maya kicked it. |

(a) 0.45 |

(b) 0.066 |

(c) 2.4 |

(d) 3.0 |

Practice 4.3.9 |
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During soccer practice, Maya kicked a soccer ball 37° off the ground at 25 m/s. Max, the goalie, caught the ball 60 m away from Maya and 1.0 m off the ground. What was the velocity of the ball when Max caught it? |

(a) |

(b) |

(c) |

(d) |

(e) |

(f) |

**Discuss!**

Consider how you would answer these questions. Then bring this to class for a group discussion.

In a carnival booth, you can win a stuffed giraffe if you toss a quarter into a small dish. The dish is on a shelf above the point where the quarter leaves your hand and is a horizontal distance of 2.1 m from this point. If you toss the coin with a velocity of 6.4 m/s at an angle of 60° above the horizontal, the coin will land in the dish. Ignore air resistance.

(a) What is the height of the shelf above the point where the quarter leaves your hand?

(b) What is the vertical component of the velocity of the quarter just before it lands in the dish?