Consider a projectile launched at a height h feet above the ground and at an ang
ID: 3214255 • Letter: C
Question
Consider a projectile launched at a height h feet above the ground and at an angle ? with the horizontal. If the initial velocity is v0 feet per second, the path of the projectile is modeled by the parametric equations x = t(v0 cos(?)) and y = h + (v0 sin ?)t - 16t2. A rectangular equation for the path of this projectile is y = 4 + x ? 0.006x2. (a) Eliminating the parameter t from the position function for the motion of a projectile to shows that the rectangular equation is as follows. y = (?16 (sec(?))^2 / v0^2)x^2 + tan(?)x + h (b) Find h, v0, and ?. (Round your answers to two decimal places.) (d) Use a graphing utility to approximate the maximum height of the projectile. (Round your answers to two decimal places.) What is the approximate range of the projectile?Explanation / Answer
Fleas are also animals, and according to the 2/15/2011 issue of the NY Times, they can jump to a height that is 38 times their body length. This is equivalent to a puma with a body length of 5 feet jumping 190 feet straight up, or about 16 times higher than the "best leaper" in your question. This is one reason that zoologists don't have much to do with physics teachers, who are also among the worst mathematicians in the animal kingdom and will often tell you that the square root of 10 is p. But I digress. The laws of projectile motion apply as well to pumas as they do to fleas, and they say that the maximum height of a projectile launched at an angle is given by: v²sin²? y = ———— 2g Where y = maximum height above the ground v = initial velocity ? = angle above the horizontal at which the projectile is launched g = acceleration due to gravity You know y = 12 feet, ? = 45°, and g = 10 m/s², so you can convert to SI units and solve the equation for v.