# Impulse acceleration directions

A post is driven into the ground by means of a blow from a pile-driver. The pile-driver falls from rest from a height of 1.6 m above the top of the post.

(a) Show that the speed of the pile-driver just before it hits the post is 5.6 m s–1.

The post has mass 6 kg and the pile-driver has mass 78 kg. When the pile-driver hits the top of the post, it is assumed that the there is no rebound and that both then move together with the same speed.

(b) Find the speed of the pile-driver and the post immediately after the pile-driver has hit the post.

The post is brought to rest by the action of a resistive force from the ground acting for 0.06 s. By modelling this force as constant throughout this time,

(c) find the magnitude of the resistive force,

...

I'm stuck on part (C), the answer is $(78+6)(g+a) = 84(9.8+86.6)$

but the accelerations caused by gravity and the force of the drop are in opposing directions; so, why are they added, instead of subtracted?

• It's just vector addition but you have to take into account of direction ofcourse – masterwarrior123 Feb 9 '17 at 1:43

The deceleration is downwards so the acceleration $a$ is upwards. If the resistive force is $F$ upwards then applying Newton's 2nd Law the net force on the pile is
$F-mg=ma$
$F=m(g+a)$.