# A projectile is shot at an angle of #pi/6 # and a velocity of # 18 m/s#. How far away will the projectile land?

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To find the horizontal distance the projectile will travel, you can use the formula:

[ \text{Range} = \frac{{v^2 \times \sin(2\theta)}}{g} ]

where:

- ( v ) is the initial velocity of the projectile,
- ( \theta ) is the angle of projection,
- ( g ) is the acceleration due to gravity (approximately ( 9.81 , \text{m/s}^2 )).

Given:

- ( v = 18 , \text{m/s} ),
- ( \theta = \frac{\pi}{6} ),
- ( g = 9.81 , \text{m/s}^2 ),

Substitute these values into the formula:

[ \text{Range} = \frac{{(18)^2 \times \sin(2 \times \frac{\pi}{6})}}{9.81} ]

[ \text{Range} = \frac{{324 \times \sin(\frac{\pi}{3})}}{9.81} ]

[ \text{Range} = \frac{{324 \times \sqrt{3}/2}}{9.81} ]

[ \text{Range} \approx \frac{{324 \times 0.866}}{9.81} ]

[ \text{Range} \approx \frac{{280.584}}{9.81} ]

[ \text{Range} \approx 28.57 , \text{meters} ]

Therefore, the projectile will land approximately ( 28.57 , \text{meters} ) away.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- A projectile is shot at an angle of #pi/12 # and a velocity of #46 m/s#. How far away will the projectile land?
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- What is the projection of # (-4i + 3k)# onto #(-2i -j + 2k)#?
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- A projectile is shot from the ground at an angle of #(5 pi)/12 # and a speed of #1 m/s#. Factoring in both horizontal and vertical movement, what will the projectile's distance from the starting point be when it reaches its maximum height?

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