A projectile is launched into the air with initial velocity 49m / s from ground at an angle of 53.13 degrees relative to horizontal. The coordinates of the projectile, (x, y) , relative to the launch point (that is, the launch point is the origin of the cooordinate system) has parametric equations x = 29.4t; y = - 4.9t ^ 2 + 39.2t where t is the time in seconds since the projectile was launched. (This model ignores air resistance.) (a) Eliminate the parameter to write y as a function of Sketch the graph of the projectile, indicating the positive orientation. (b) Find the time when the tangent line to the parametric curve is horizontal. Then find the value of y at this time. That is the maximum height of the projectile. (c) Find the total distance traveled by the projectile; that is, find the arc length of the parametric curve. If you don't round anything, then after simplifying and completing the square the integral will look like , which is something we learned how to do using trig substitutions a * integrate sqrt(u ^ 2 + b ^ 2) du from t_{1} to t_{2}

A projectile is launched into the air with initial velocity 49.0 m/s from ground at an angle of 53.13 relative to horizontal. The coordinates of the projectile, (x, y), relative to the launch point (that is, the launch point is the origin of the cooordinate system) has parametric equations x = 29.4t y = -4.9t2 + 39.2t where t is the time in seconds since the projectile was launched. (This model ignores air resistance. ) (a) Eliminate the parameter to write y as a function of x. Sketch the graph of the projectile, indicating the positive orientation. (b) Find the time t when the tangent line to the parametric curve is horizontal. Then find the value of y at this time. That is the maximum height of the projectile. (c) Find the total distance traveled by the projectile; that is, find the arc length of the parametric curve. If you don't round anything, then after simplifying and completing the square the integral will look like ta a Vu2 + 62 du, which is something we learned how to do using trig substitutions