A point B is 80 m north of a point A on a horizontal field - Leaving Cert Applied Maths - Question 2 - 2021

To find t, we can use the distance formula and the relationship of the movements of Alan and Brian.

• Alan's distance after time t is given by:

  • Distance = Speed × Time
  • Distance = 2.5 m/s × (t + 8 s)

• The horizontal and vertical components of Alan's movement can be described as:

  • Horizontal component (North-East):

  • Vertical component (North):

• Brian starts running after 8 seconds, so his distance after t seconds will be:

  • Distance = 4 m/s × t

Setting up the equation using the Pythagorean theorem to find t:

$(4t)^2 = 80^2 + (2.5(t + 8))^2 - 2 × 80 × 2.5(t + 8) cos(45)$

On simplifying:

$16t^2 = 6400 + 6.25(t^2 + 16t + 64) - 400(t + 8)$

After equating and solving:

$t = 14.15 ext{ seconds}$