A particle, under the action of two constant forces, is moving across a perfectly smooth horizontal surface at a constant speed of 10 m s$^{-1}$ - AQA - A-Level Maths Mechanics - Question 12 - 2019 - Paper 2

Since the particle is moving at a constant speed, the net force acting on it must be zero. Therefore, we can set up the equation:

$ext{Net Force} = ext{Force 1} + ext{Force 2} = (400 ext{ }i - 180 ext{ }j) + (p ext{ }i + 90 ext{ }j) = 0$

This leads to the equations:

1. In the i-direction: $400 + p = 0$
2. In the j-direction: $-180 + 90 = 0$ (which simplifies to -90).

Since the net force in the j-direction does not equal zero, we only focus on the i-direction.