Projectile Motion- magnitude of final velocity

[Nelson2436]

Homework Statement

Consider a cannon on a 50m high cliff. The cannon shoots a cannonball with an initial speed of 200m/s at an angle of 30°, causing the cannonball to land 41m away from the cannon. What is the magnitude of the velocity of the cannonball the instance just before it hits the ground?
a) -205m/s
b) 205m/s
c) 173m/s
d) 267m/s

Homework Equations

a_x=0 a_y=-g
1) X_f=X_i+V_ixt
2) Y_f=Y_i+V_iyt-½gt²
3) V_fy=_Viy-gt
4) V_fy²=V_iy²-2g(Y_f-Y_i)

The Attempt at a Solution

V_i=200m/s
V_ix=200cos30 V_iy=200sin30
X_i=0m Y_i= 50m
X_f=41m Y_f= 0m

In order to find the magnitude of V_f, I need to find its components, V_fx and V_fy. In projectile motion, V_fx=V_ix=200cos30, so I just need to find V_fy.

Using equation 1 to find time: t=41/(200cos30)= 0.2367s
I then plugged time into equation 3 to find V_fy=200sin30-(9.8)(0.2367)= 97.68m/s

So V_fx=200cos30= 173.2m/s and V_fy= 97.68m/s so
V_f= √(V_fx²+V_fy²)= √(173.2²+97.68²)= 199 m/s

I don't see where I'm going wrong, but 199m/s is not one of the 4 multiple choice answers. I would greatly appreciate any help.

 

[TSny]

Hi, Nelson2436. Welcome to PF!

The 41 m given in the problem just doesn't seem right. You should actually be able to find where the cannon ball lands from the other information given in the problem. Did you state the problem exactly as given?

 

[Nelson2436]

Yes, I stated the problem exactly as given. This problem is driving me crazy.