Professional golfer Nancy Lopez hits a golf ball with a force to produce an intinial velocity of 175 feet per second at an angle of 35 degrees above the horizontial. She estimates the distance to the hole to be 225 yards.

A) Write the position of the ball as a pair of parametric equations. (I know that it is x=175tcos(35)and y=175tsin(35)-1/2gt^2)

B) Find the range of the ball. (I cannot seem to get the correct answer.)

Solution Preview

Please note the corrections at the end of the problem.

A.)
Because,
r*cos(Q) = x =175*t*cos(35) ....(1)
and,
r*sin(Q) =y = 175*t*sin(35)-1/2gt^2) .....(2)

where, read Q as theta.
Square (1) and (2) and add them:
r^2 = (175*t)^2 + g^2*t^4/4 - 175*g*t^3*sin(35)
=>r^2 =30625*t^2 + 256*t^4 - 3212.028*t^3 --Answer

NOTE: g = 32 ft/s^2

Eqn ...

Solution Summary

Parametric equations are used to solve a position and range problem.

Polar and Parametric Equations : Eliminate the parameter to find a cartesian euqation of the curve; sketch the curve with the given polar equation. ...

... by the range Our circle equation is: (1.12) This means that the center is located at and the radius is . Hence, the general parametric equations of this circle ...

Equation of closed curve in xy plane and its parametric form. The equation 49x^2 + 36y^2 = 1764 describes a certain closed curve in 2-dimensional space. ...

... (please see attachment for equation). ... 1. Find a parametric representation of the curve ... 3. Find the equations of the tangent (straight line) and the normal plane ...

... has rank 1 is the curve with parametric equations x = t ... Continuing to solve the system of equations gives us z = x3 (plug y = x2 into the second equation). ...

... Write a parametric equation for your position after t seconds. 7. Using parametric equations and simple trigonometric identity, find the angle that will ...

...equation of the plane is. x + 2y - 2z = 1. Now the line passes through the points A = (3, 5, 8) and B = (7, 13, 22), so it satisfies the parametric equations. ...

... for the length of vectors, general solutions of differential equations, and solutions ... where Γ is a line (curve) defined by the parametric equation: rr r rr r ...