# How do you answer this A level physics projectiles question?

One record suggests that the maximum horizontal distance an arrow has been shot on level ground is 889m. Assuming it was shot at 45o, with what initial velocity did it leave the bow?
Original post by CHAYMA0
One record suggests that the maximum horizontal distance an arrow has been shot on level ground is 889m. Assuming it was shot at 45o, with what initial velocity did it leave the bow?

Approach with every SUVAT question by listing out all the equations:
s = ut + (1/2)at^2
v = u + at
v^2 = u^2 + 2as
(there are other variations, but the above is adequate)

u will require you to take account of the angle of the projection as well
horizontal u = ucos45 = u(sqrt(2)/2)
vertical u = usin45 = u(sqrt(2)/2)

The only common component that links the horizontal and the vertical is time t, so you would need to find an equation that has this factor in it. I recommend s = ut + (1/2)at^2 in both your horizontal and vertical distances.

Horizontal a = 0. Vertical a = g (however you measure it e.g. 9.8m/s, 10 m/s)

The missing piece of information that I don't have is how high the initial starting position was (1m? (1.5m? Unless they were super tall/short), as there's very little possibility that the arrow was shot night next to the ground. If you have this, you should be able to find out u.
The height of the bowman is probably not significant in this calculation. Although of course it does affect the range slightly.
Any error introduced by not considering its value (Say, max 2m height) is in the 3rd significant figure. (The range is 889m and the max height reached is over 200m, when you do this calculation.)
So you would need to take g = 9.81 m/s/s and quote the angle as 45.0 degrees to justify worrying too much about the starting height of the arrow and giving the answer to 3 sig figs.
For A-level physics (I assume this is) then the height of the bowman would probably be ignored.

Added: A quick calculation shows that increasing the initial height of the arrow by 1 m increases the range by about 1 m.
(edited 1 year ago)