A particle is projected horizontally at 10ms-1 from a height of 45m. Calculate the horizontal distance covered by the particle before hitting the ground. Take g -10ms-1

Your problem is mostly vertical. In the horizontal direction it simply goes straight ahead during the fall.

so
How long to fall 45 meters?
h = Hi + Vi t -(10/2) t^2
0 = 45 + 0 * t - 5 t^2
so
t^2 = 9
t = 3 seconds
Now the thing goes horizontal for 3 seconds at 10 m/s
about 30 meters :)