# A projectile is shot at an angle of #pi/3 # and a velocity of # 46 m/s#. How far away will the projectile land?

Range of a projectile at 60 degrees

The formula yields the projectile's range.

Adding up all the values gives us a range of 122.78 meters.

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To find the horizontal range of the projectile, you can use the formula:

[ R = \frac{{v^2 \sin(2\theta)}}{g} ]

where:

- ( R ) is the horizontal range,
- ( v ) is the initial velocity of the projectile (46 m/s),
- ( \theta ) is the angle of projection (( \pi/3 )),
- ( g ) is the acceleration due to gravity (9.8 m/s(^2)).

Substituting the given values:

[ R = \frac{{(46)^2 \sin(2(\pi/3))}}{9.8} ]

[ R \approx \frac{{2116 \times \sqrt{3}}{2}}{9.8} ]

[ R \approx \frac{{2116 \times 1.732}}{19.6} ]

[ R \approx \frac{{3662.192}}{19.6} ]

[ R \approx 186.7 , \text{m} ]

Therefore, the projectile will land approximately 186.7 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.

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