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Projectile Motion

When an object is thrown, gravity acts upon it and affects the path traveled.

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Have you ever seen a cartoon where a character runs off a cliff and stops midair untill they realise they are going to fall, and then fall straight down? Is it really possible for that to happen? To find this we need to find the horizontal projectile motion.

Let's assume the coyote travels at 25 mph from a height of 25 miles. What can we say about the velocity of the object as it reaches the ground.

First we must find the time the coyote remained suspended midair. 

To find that number we use the equation 

d = vit + 1/2 at2   

but since there is no initial velocity we only need 1/2 at2   .

therefore \begin{align*}t=\sqrt{2d/a}\end{align*}

t=2.23 minutes.

We can now use d=rt to find the distance it landed from the base of the mountain.


d=55.75 miles from the base of the mountain



\begin{align*}V=22.360679775 \end{align*}

Now to find the velocity you require an angle. To find this we must imagine a triangle. With both the opposite and adjacent side being 25 we know that the angle can be found by using cos.

Therefore we know the \begin{align*}\cos\theta=25/35.3553390593\end{align*}

we can find therefore that the angle is 70 degrees.

The coyote will travel at 22.360679775mph at a slope of 70 degrees.

This may seem like good news to you that you can solve these questions now but it is all bad for the coyote.

Creative Application:

1. When might this skill be used in the real world?

2. What other forces may have affected the coyote's descent?

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