Projectile Motion- magnitude of final velocity

AI Thread Summary
The discussion revolves around calculating the final velocity of a cannonball shot from a cliff at a specific angle and speed. The initial calculations yield a final velocity of approximately 199 m/s, which does not match any of the provided multiple-choice answers. Participants suggest that the horizontal distance of 41 m may be incorrect, indicating a potential error in the problem setup. The user expresses frustration over the discrepancy and seeks clarification on the calculations. The conversation highlights the importance of verifying problem parameters in projectile motion scenarios.
Nelson2436
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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


ax=0 ay=-g
1) Xf=Xi+Vixt
2) Yf=Yi+Viyt-½gt2
3) Vfy=Viy-gt
4) Vfy2=Viy2-2g(Yf-Yi)

The Attempt at a Solution


Vi=200m/s
Vix=200cos30 Viy=200sin30
Xi=0m Yi= 50m
Xf=41m Yf= 0m

In order to find the magnitude of Vf, I need to find its components, Vfx and Vfy. In projectile motion, Vfx=Vix=200cos30, so I just need to find Vfy.

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

So Vfx=200cos30= 173.2m/s and Vfy= 97.68m/s so
Vf= √(Vfx2+Vfy2)= √(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.
 
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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?
 
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Yes, I stated the problem exactly as given. This problem is driving me crazy.
 

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