Solving Physics Problems - Aiming a Gun at a Target

[lmf22]

physics problem...

A hunter aims directly at a target (on the same level) 100m away.
a) If the bullet leaves the gun at a speed of 250m/s, by how much will it miss the target?
b) At what angle should the gun be aimed so the target will be hit?

Any help would be great. Thanks.

 

[arildno]

What have you done so far?

 

[lmf22]

I set up the axis where the hunter is Y meters up and the target is also Y meters up to 100m to the right.
The X component of the velocity is 250m/s and Y component is 0.

For part a)
I used the distance formula in the Y and X components so:
Y = Yi + vi*t + 1/2*a*t^2.
X = Xi + vi*t + 1/2*a*t^2.

Y=0
Vi=0
Xi=0
a in the X component = 0

From the X component of the distance formula I solved for time =0.4s.
Then I plug in the time into the Y component of the distance formula and got 39.2m.

I'm not sure where to start for part b).

 

[arildno]

Note that given initial speed V0, and angle a to the horizontal, we may write:
Initial horizontal velocity: V0cos(a)
Initial vertical velocity: V0sin(a)

Find the time T from the horizontal component (that is, which yields final horizontal position equal to 100)
Determine a by requiring that at this time T, final vertical position must be zero (equal to initial level)