Officer R. Ingling,
I appreciate you trusting my calculus professor’s recommendation. Hopefully I won’t disappoint. Let’s go over the issue at hand again. Bobo the clown was shot out of a cannon, across a canyon, and into the canyon wall, killing him. You have a suspect in hand, the owner of the traveling circus in which Bobo worked, Mr. Rasterdly, who was near when Bobo’s cannon was shot and who you assume to have been the one to press the button to shoot the cannon. However you would like to be sure that Mr. Rasterdly shot the cannon and that it wasn’t a potential suicide before you lock him away.
Let’s also go over some of the technical information you’ve given me. One end of Bobo’s cannon is three feet off the ground and the whole cannon…show more content… Because 1 meter = 3.28 feet, we’ll just divide the feet by 3.28 to get our new measurements. 5ft3.28ft = 1.524 meters 3ft3.28ft = 0.915 meters A moving object’s position is given by the vector-valued function r(t) = for t0, the object’s velocity is the derivative of the position which is given by v(t) = r’(t) = , and the speed of the object is given by |v(t)| = x’(t)2+ y’(t)2(Briggs, 834). To find x(t) and y(t) we’re going to use the information we have on the cannon. Let’s visualize it as a triangle, like so: We’re looking for the angle marked so to find it we use the formula for sin(x) which tells us to take the opposite value (0.915m) over the hypotenuse value (1.524m) and plug it into a formula using arcsin, which will give us the angle. So we have: sin-1(x) = 0.9151.524= 36.9 Now to find the horizontal and vertical vectors, or x(t) and y(t), we’re going to use the speed at which the cannon fired Bobo (30mps) and the angle we just found. For x(t) we use cosine because it’s going in a horizontal direction and for y(t) we use sine because it’s going in a vertical direction. Our formulas are as follows: x(t) = 30cos36.9 = 24 y(t) = 30sin36.9 = 18 Next to find