Calculating Launch Speed for a Catapult with Drag Force

[juju1]

Homework Statement

Two students, Joe and Jane Fisycks, make a catapult. They use a spring with a spring constant of 101 N/m to launch a tennis ball. When the catapult is loaded, the spring is stretched 0.477 m. This is also the distance the tennis ball travels as it is being fired by the catapult. When loaded, the tennis ball is at ground level. When it leaves the catapult, it is 0.567 m above ground level. A drag force D acts on the tennis ball as it is being fired. The tennis ball's mass is 0.0579 kg.

(e) If there were no drag, what launch speed would the tennis ball have? (find v_1)

Homework Equations

The Attempt at a Solution

so i found the equations when it is ready to fire and after it fires
.5kx^2 and (.5mv_1^2)+(mgy_1)+Dx

i put these two equations together to solve for v_1, yet I still am not getting a right answer.

my v_1 equation is sqrt( (.5kx^2 - mgy_1) / (.5m) )

i plugged in 101N/m for k
0.477 m for y_1
0.0578 for m
9.8 for g
0.567 for x

what am i doing wrong?

 

[TSny]

Looks like you might have switched the values of x and y₁.

 

[juju1]

so 19.659 m/s?

 

[TSny]

so 19.659 m/s?

I believe that's right. Note that the mass is given to be 0.0579 kg, but you later wrote 0.578 kg. (Not a very significant difference.)

How many significant figures should the answer have?

 

[juju1]

3 sigfigs! So rather: 19.7 m/s

 

[TSny]

3 sigfigs! So rather: 19.7 m/s

Yes. That's essentially what I got, too. (19.6 m/s)