Mechanics 1 projectiles Q

I have a M1 exam in January and I am very stuck on part 3 and part 4 of this question.







Please help!

iii) two parts are always the same height because they both (after explosion) have 0ms-1 vertical velocity and accelerate uniformly due to gravity (recall horizontal and vertical components are independent)

because of this, the only difference between the two parts is the horizontal distance between them

now find expressions for the distance travelled by the two parts after time t and the subtract the expressions for the distance between them

iv) plug the times into the above expression to calculate the distance between them for the times when they hit the ground (by symmetry, this is just twice the time it took to reach the maximum)

and the time it takes both to be 10m above the ground (i.e. calculate the time it takes the projectiles to fall 30m using $s = ut + \frac{1}{2}t^{2}$) and plug it in to the expression

Thank you for your help but I need to ask some questions.

How do you know both parts have 0ms-1 velocity after explosion?

For part 3, I have got two expressions but I don't think they are anything like the answer in the mark scheme. I have s=21t and s=13.125t.
On the markscheme how have they got 0.75x21t=15.75t ?

I really appreciate your help!

1) well since it explodes instantaneously at the maximum (where the vertical velocity = 0), it can be assumed the only velocity it has is the horizontal component

2) one of the expressions for the displacement is 21t, the other is 1/4 x 21t which should be 5.25t

and 21t - 21/4t is the same as 21t x 0.75

it's alright sweet cheeks