Time of flight for projectile with non-zero initial velocity

[so_gr_lo]

Homework Statement

Find time of flight of particle projected down at 10° to horizontal at initial speed 20 ms^-1 at height 10m.

Relevant Equations

s = ut -1/2at^2

These questions normally have initial velocity = 0, so that one of the t terms cancels. In this case u = 20ms^-1 so I end up with a quadratic. Which is fine if I plug it into the quadratic formula as one result is -ve so can be ignored, while the other gives t as +ve. just wondering if this is the correct way of calculating the time of flight. Attempt at question below

 

[Doc Al]

Looks good to me. (All that matters is the vertical motion.)

 

[haruspex]

Homework Statement:: Find time of flight of particle projected down at 10° to horizontal at initial speed 20 ms^-1 at height 10m.
Relevant Equations:: s = ut -1/2at^2

These questions normally have initial velocity = 0, so that one of the t terms cancels. In this case u = 20ms^-1 so I end up with a quadratic. Which is fine if I plug it into the quadratic formula as one result is -ve so can be ignored, while the other gives t as +ve. just wondering if this is the correct way of calculating the time of flight. Attempt at question below

View attachment 274557

Yes, that's the right way.
The reason you also get a negative solution is that your equation represents an entire parabola in which, at t=0, the particle is moving down at the given angle, speed and height. So it will be at the target height twice, once before t=0 and once after.