**1. The problem statement, all variables and given/known data**

) You are given the task of shooting a tennis ball from ground level through 2 hoops. The two hoops’ centers and the launch site are located in the same vertical plane, and the hoops are oriented perpendicular to the ball’s proposed trajectory and also in a vertical plane.

The first hoop has a height y1 and is located at a horizontal distance from the x1 launch site (which is located at x0, y0). The second hoop is located at x2, y2.

a) Use the d-v-a-t formulas to eliminate time and solve for the y-position as function of the x-position. In particular, show that

y = a x + b x2

Identify the quantities

**and**

*a***in terms of launch speed**

*b***and launch angle**

*v0***, and the gravitational field strength**

*q0***(which will later take on the value of 10 m/s2).**

*g*b) Solve for a and b in terms of x1, y1, x2, and y2.

c) For the case of y1 = 4.0 m, x1 = 2.0 m and y2 = 3.0 m, x2 = 4.0 m, determine the values of

**and**

*v0***.**

*q0***2. Relevant equations**

y = Vy*t + .5(g)(t)^2

x = Vx*t

Vx = Vocos(theta)

Vy = Vosin(theta)

**3. The attempt at a solution**

I've solved the a) part of the question and gotten that the coefficient a = tan(theta) while the coefficient b = g/(2*(Vocos(theta))^2). I'm not sure how to put these two equations in terms of the position coordinates x1, x2, y2, and y1.