Expert: Scott A Wilson - 11/10/2009

Question
I'm not even sure how to start this. I took a stab at it but this just doesn't look right. I'm going back and taking an algebra class and I'm pretty sure that the equation should be for a parabola.

Here is my work:

For a cannon, the range R = V0^2sin(2A)/g and the height h = V0^2sin^2(A)/(2g)
where V0 is the initial velocity and A is the angle of the cannon above the horizon.  
Putting in the given values for R and h, V0 = 41.2m/s and A = 56.3 degrees
The vertical distance,y, as a function of time = (V0sinA)t -(1/2)gt^2 and the horizontal distance,x, as a function of time = (V0cosA)t.




Here is the question:

On July 23, 1997, Washington County, in Oregon was advertising their Fair & Rodeo special attraction on the Internet: "As the countdown begins, David Smith, Jr. - THE BULLET - puts on his safety helmet, slides down the slender barrel of the cannon, positioning himself to become a human projectile. Then begins the countdown and the announcer asks the audience to cover their ears as protection from the noise of the blast. Three! Two! One! FIRE! David Smith, Jr. - THE BULLET - blasts into the air, reaching a height of 60 feet above blast off and landing safely in his pre-positioned safety net at a distance of 160 feet. This is a death-defying stunt to send shivers down your spine!"


Use the given information and assume that the tip of the cannon is at the same level as the pre-positioned safety net to find the equation of the flight of David Smith, Jr. aka THE BULLET!




I could use any kind of insight. Your help is much appreciated. Thank you.

Answer
Take the Angle as A, the Range as R, and the Height as H.

We know R = 160 = V0•cosA and H = 60 = V0•sinA.

For R, we know that 1 = V0•cosA/160 and for H, we know that 1 = V0•sinA/60.

Since now both equations are equal to 1, then can be set equal.

Multiply both sides by 60/cosA and you'll get a constant = sinA/cosA = tanA.

Solve for A.