Trignometry question?

Question

I am stuck on this question and i am hoping someone could provide some guide on understanding it:

A human cannonball is shot from a cannon at the county far. He reaches a height of 60 feet before landing in a bet 160 feet from the cannon. Sketch the graph of his path and then find the equation of the graph.

Answer 1

To find the equation, you need to find the initial velocity.

The vertical component of velocity may be found as:
vf^2 = vi^2 + 2ad
0 = vi^2 + 2 * -9.8 * 160 ft
0 = vi^2 - 3136
vi^2 = 3136
vi = 56 ft/sec (vertical)

The time, therefore can be found using the equation
d = vit + 1/2at^2
0 (because it hits the ground) = 56 * t + 1/2 * -9.8 * t^2
0 = 56t - 4.9t^2 (divide by t...)
0 = 56 - 4.9t
4.9t = 56
t = 11.429 sec.

Now that we know t, the vertical distance can now be defined as: y = 56t - 4.9t^2

The horizontal distance can be defined as: x = v * t
v = d/t = 160 / 11.429 = 14 ft/sec
x = 14t

Now, we can substute x for t to find a classical graphing function where y = f(x):
t = x/14
y = 56t - 4.9t^2
y = 56 (x/14) - 4.9(x/14)^2

y = 4x - 0.01701x^2 (solution!)

Answer 2

Assume that the human cannon ball is shot from point A

The height of 60 feet is point B and where he landed is point C.

Draw a line from point A to point C = 160 feet
Draw a line from point C to point B = 60 feet
Draw a line connecting point A to point B

You can then resolve the equation i.e. to get the distance of point A to B based on the Pythagorean Theorem formula

Answer 3

imagine a triangle is a=60 and b=160 solve for c
c=square root of 60*60+160*160 do the math!