# Parametric Equation

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.)

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#### 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.