# A projectile is shot at an angle of #pi/8 # and a velocity of # 8 m/s#. How far away will the projectile land?

Range =

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

Range = (Initial Velocity^2 * sin(2*Theta)) / g

Where:

- Initial Velocity is the initial speed of the projectile.
- Theta (θ) is the angle at which the projectile is launched.
- g is the acceleration due to gravity (approximately 9.81 m/s^2).

In this case:

- Initial Velocity (v) = 8 m/s
- Angle (θ) = π/8 radians
- Acceleration due to gravity (g) = 9.81 m/s^2

Plugging these values into the formula:

Range = (8^2 * sin(2*(π/8))) / 9.81

Calculating the value:

Range = (64 * sin(π/4)) / 9.81

Range = (64 * √2/2) / 9.81

Range = (64 * 0.7071) / 9.81

Range = 45.2564 / 9.81

Range ≈ 4.62 meters

So, the projectile will land approximately 4.62 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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