Final answer:
The parameter is eliminated by expressing t in terms of x and then substituting into the equation for y, resulting in a parabola. Projectile motion equations and the quadratic formula are used to calculate unknowns in their respective contexts.
Step-by-step explanation:
To eliminate the parameter and find a rectangular equation for the curve described by the parametric equations x = t and y = t2 + 1, we can express t in terms of x and then substitute it into the second equation for y. Since x = t, we have t = x. Substituting this into the equation for y gives us y = x2 + 1, which is an equation of a parabola that opens upwards.
When dealing with projectile motion problems, such as scenarios where one needs to find the vertical position (y) as a function of time (t), the equation often used is y = yo + vot + ½at2 where yo is the initial vertical position, vo is the initial vertical velocity, a is the vertical acceleration, and t is the time elapsed. To solve for a using known values, one would plug in the given information and solve for the unknown.
The quadratic formula can be applied to solve quadratic equations of the form ax2 + bx + c = 0, where a, b, and c are coefficients and x represents an unknown variable.