Would somebody be so kind as to help us out? (projectile motion)

You need to work out the time of flight in terms of the sins and cos's using the y equation and then put that time into the x equation. Like so:

Let the angle = a

y = ut + 0.5at^2
y = 150t sina - 0.5gt^5 = 0 when the projectile hits the ground

hence t = (300 sina) / (g)

x = ut + 0.5at^2
x = 150t



1500 = 150(300)sina / g

a = sin-1 (1500g / 45000) = 19 degrees

Wouldn't you need to resolve the initial velocity into its horizontal and vertical components to do it like this?

You need to work out the time of flight in terms of the sins and cos's using the y equation and then put that time into the x equation. Like so:

Let the angle = a

y = ut + 0.5at^2
y = 150t sina - 0.5gt^5 = 0 when the projectile hits the ground

hence t = (300 sina) / (g)

x = ut + 0.5at^2
x = 150t cosa

1500 = 150(300)sina.cosa / g

sina.cosa = 1500g / 45000
0.5 sin (2a) = 1500g / 45000 (Using a mathematics identity)
2a = sin-1 (3000g / 45000)
a = 0.5 sin-1 (3000g / 45000)
a = 20.4 degrees

I doubt a physicist would be expected to solve that equation.

According to my book the angle is 15 degrees, although it's been wrong before. The question was apparantly on a past paper, so... I still don't really understand tbh but thanks for your effort. + rep for everybody who helped in the next few days. Argh, so much to learn in so liittle time...