Question

Really need help with 1) How fast was Stan going at the time of impact?

Stan the Man, from the local circus, was a human cannon ball. While practicing one day, he was shot out of a cannon and into a canyon and subsequently died. It is believed it was murder but suicide cannot be ruled out, yet. Here are the facts of the case One afternoon, Stan climbed into the cannon for reasons we do not know. According to eyewitness accounts, the only living beings within close range were the owner of the circus, Ringmaster Rick and five lephants. Somehow the cannon was fired, and Stan, who was not wearing a parachute, was shot clear acros the gorge, hitting the opposite wall some 250 meters down. We do not know how far it is across the canyon but it must be at least 200 meters. The cannon is not very large; when one end is on the ground, the other end is only 4 feet in the air and from base to mouth it is only 5 feet long. Nonetheless, it can fire off something as large as a human being at a speed of 25 meters per second The main line of questioning has been whether Stan fired the cannon himself or whether Ringmaster Rick set it off instead. It only takes about a half a second to push the button. There is one eyewitness who ears that Ringmaster Rick hit the ignition button. We have another who swears that Ringmaster Rick kept his hands to himself. There are witnesses who swear that Ringmaster Rick and Stan had been arguing about money and others who claim they are best friends Here is Ringmaster Rick's version of what happened I was filming the elephants for a rock video. Stan was in the cannon checking things out to make sure everything was working properly. I was paying attention to the elephants and we were getting to the tricky part of them standing on their hind legs when I heard "boom". I turned around and there is Stan sailing off. I kept waiting for his chute to open but his chute never does. He bangs into the wall on the opposite side and tumbles can't believe it is suicide. It must have been an accident. He pushed the button by mistake The video recorder confirms his story up to a point: it has no sound, but it has a digital clock which it turns out that we know a bit more. Stan's watch had been fixed in town that week and he had just leaves an imprint on the film. Just as the elephants were rearing up (15:55:20 on the film) the camera veered and was dropped. picked it up the morning of his death. The watchmaker said it was keeping perfect time since she repaired it Stan was wearing his watch when he died and it stopped at 3:58:53. We compared the video camera and the watchmaker's clock and found the former to be 3 minutes and 13 seconds slov There are three questions we need to answer before we can think about whether it was murde r or not 1) How fast was Stan going at the time of impact? 2) Does the time discrepancies between the watch and video recorder matter? 3) How far across the gorg e did Stan fly according to Stan's watch and according to the video recorder?

Answer 1

To find the angle at which Stan was projected:

We are given the length of the cannon and also how high off the ground one end was. we can use that along with basic trigonometry to fond the projectile angle

so we have $sin \theta = \frac{4}{5}$

therefore

in5 53.1353°

and we are also given the initial velocity u = 25 m/s

For a projectile motion from a cliff we shall refer to this general schematic:

So R = 200 m

H = 250 m

v = 25 m/s we can resolve this into two components

ul u- u cos 0 Resolution of components of velocity ()

  

7L

and   

ITL

and $\theta = 53 \degree$

We'll use another kinematics equation to determine the final y-velocity.

where g = 9.8 m/s² is the acceleration in the y- direction (due to gravity)

therefore

1,2,, 202 2 × 9.8 × 250

so

U5300

therefore

ツ,,-V5300 = 72.8

The x-velocity can also be determined using a similar equation to (1)

here the x-direction acceleration is not given (usually we have to consider the drag due to wind but we are going to ignore that in this problem) so since there is no acceleration is x direction the x component of velocity stays the same.

uf,,-u! = 15 m

Now we shall find the magnitude of the final velocity using the Pythagorean theorem:

TL vf- V152+72.82 74.32