Projectile motion and SUVAT equations

[mathsman]

Attempting a projectile motion question where initial and final speed is given but angle of elevation isn't. Need to find an equation for the vertical distance H travelled. I got the right answer using v^2 = u^2 + 2as substituting s=H and a=-9.8.

However the mark scheme states that this SUVAT equation can't be used as this equation needs the vertical component of speed (as gravity only acts vertically) . The correct answer was to use conservation of energy principle ie initial KE = final KE + GPE. However if I use this energy equation I get the following: 1/2 mu^2 = 1/2 m v^2 - 2gH . Multiplying throughout by 2 and re-arranging this gives v^2 = u^2 + 2as ! In other words the conservation of energy equation gives me the SUVAT equation which I'm not supposed to use! Where is the mistake??

 

[Doc Al]

Not really a mistake. It's that you haven't justified your use of the SUVAT formula. It does turn out to work fine in this case, but it's intended use is for motion along a line so the velocities are supposed to be the components along that line.

 

[Doc Al]

This is justified: $v_y^2 = u_y^2 + 2as_y$

But since $v_x = u_x$, you can add $v_x^2 = u_x^2$ to both sides, giving $v^2 = u^2 + 2as_y$.

But conservation of energy gives it to you immediately.

 

[mathsman]

Many thanks to you both. I think I may have done a similar question many years ago and remember using the standard v2=u2+2as equation but couldn't remember why it worked ! Obviously adding the square of the horizontal component to both sides makes it clear why it does in fact work. The mark scheme simply gave no marks for using SUVAT so although my calculated value for h was correct I lost method marks. Presumably if I had 'justified' why I could use it that would be ok (although I'm never sure how far examiners give marks for methods that aren't in the mark scheme!.

Having said that the conservation of energy approach is much neater anyway (dont know why I overlooked it! - normally exam questions hint at using conservation of energy principle but this time it ddn't!