1. Police Department
Constabulary Avenue
Big City, PU 11234
2 November 2015
Math 225 Volan Nnanpalle
Bloomsburg University
Bloomsburg, PA 17815
Dear Police Department:
I have received your letter about the death of a circus clown. The mystery of
whether he was murder grabbed my attention because I love to solve mysteries. By
sending me this problem you have made an important step in solving this mystery.
I will clearly answer all questions, state methods being used to formulate my
answers and cite my findings.
These are your questions I plan to answer in my report:
1) “Does Rasterdly’s storyhold water, and can we convince the jury that it
doesn’t?”
Rasterdly’s story does not hold water and we can convince the jury that it does
not.
2) “How fast was Bobo going at the time of impact, and was this sufficient
to cause death?”
Bobo was going 81.4meters/sec or 293.4 kilometers/hour, this was sufficient to
cause death.
3) “How far across the gorge Bobo flew?”
Bobo flew 240m across the gorge.
- Now let’s solve this mystery!

2. Proofs
Quadratic formula
Source: Proof of the Quadratic formula
Formula of Dynamics
Let u = initial velocity in m/s
Let s = distance traveled in m
Let v = final velocity in m/s
Let a = acceleration in m/s^2
Source: Formula of Dynamics
Let a, b and c be constants

3. Solution
(1)
sin (x) =
𝑂
𝐻
sin (x)=
.914
1.524
=36.9
30sin (36.9) = 18.0m/s = vy
30cos (36.9) = 24.om/s = vx
310m
240m
24m/s
18m/s
.914m
m = meters v = velocity
O = opposite km/s = kilometer per second
H = hypotenuse s = second
m/s = meters per second t = time
𝒗 𝟎 = original velocity d = distance
a = acceleration
*To determine the angle I used the length
and height of the barrel. Then I used the
angle and muzzle velocity to determine the
horizontal and vertical velocities.
*Then I proceeded to determine
Bobo’s final downward and
horizontal velocity. I used my
findings to determine his final
velocity, a velocity which was
more than enough to kill him.

4. 𝑣2
= 𝑣0
2
+ 2𝑎𝑑
𝑣 = [𝑣2
+ 2𝑎𝑑].5
𝑣 = [−18 + 2(−9.8)].5
= [(−310).5
]
= 77.8𝑚/𝑠(down)
𝑣(ℎ𝑜𝑟𝑖𝑧) = 24.0𝑚/𝑠
𝑎2
+ 𝑏2
= 𝑐2
[ 𝑎2
+ 𝑏2] = 𝑐
[24.02
+ 77.82
].5
= 81.4𝑚/𝑠
= 293.4𝑘𝑚/ℎ
In my calculations Bobo’s airborne time was determined to be 10 seconds and his speed on
impact to be 81.4 meters per second or 293.4 kilometer per hour. This speed was more than
enough to result in death. I proceeded to determine whether it was murder or suicide. Bobo
collided with the cliff-face at precisely 15:56:50. The suspect submitted a video as his alibi. The
video showed, accounting for the fact that it was four minutes sixteen seconds slow, that Bobo
was launched from the cannon at 15:56:36. By then working backwards from the initial impact
of 15:56:50, a 10 second flight would have required a launch at 15:56:40. The fact that these two
times do not match proves that the suspect forged the footage. In my investigation I mad a few
assumptions: I assumed a constant gravitational acceleration of 9.8m/s^2, I assumed no air
resistance, and I also assumed that the measurement I was provided were 100% accurate.
15:56:50
15:56:50
- 00:00:10
15:56:40  15:56:36
4s
*My discovery clearly proves that
Rasterdly forged his alibi
*By using the quadratic formula I
was able to determine Bobo’s
flight time.
𝑑 = 𝑣0 𝑡 + .5𝑎𝑡2
. 5𝑎𝑡2
+ 𝑣0 𝑡 − 𝑑 = 0
. 5(9.8) 𝑡2
+ 18𝑡—310 = 0
{
−𝑏
−[ 𝑏2 − 4𝑎𝑐].5
} ∗
1
2𝑎
{
−18
−[182 − 4 ∗ .5 ∗ 9.8 ∗ −310].5
} 9.8
𝑡 = 6.3𝑠 𝑜𝑟 𝟏𝟎. 𝟎𝒔

5. Work Cited
"Cannon Drawing." Cannon Drawing. N.p., n.d. Web. 05 Nov. 2015.
"Formula Dynamics." Formula Dynamics. N.p., n.d. Web. 05 Nov. 2015
"Proof of the Quadratic Formula." Proof of the Quadratic Formula. N.p., n.d. Web. 05 Nov.
2015