# A projectile is shot from the ground at a velocity of #84 m/s# and at an angle of #(7pi)/12#. How long will it take for the projectile to land?

To find the time it takes for the projectile to land, you can use the equation for the horizontal motion of a projectile: ( t = \frac{2v_0 \sin(\theta)}{g} ), where ( t ) is the time of flight, ( v_0 ) is the initial velocity, ( \theta ) is the angle of projection, and ( g ) is the acceleration due to gravity (approximately ( 9.8 , \text{m/s}^2 )). Plugging in the given values:

( v_0 = 84 , \text{m/s} ) ( \theta = \frac{7\pi}{12} )

( t = \frac{2 \times 84 \times \sin\left(\frac{7\pi}{12}\right)}{9.8} )

( t \approx 13.48 , \text{s} )

So, it will take approximately 13.48 seconds for the projectile to land.

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We are asked to calculate the landing time of a projectile given its initial velocity.

We can use the kinematics equation to accomplish this.

where

Entering values that are known, we have

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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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