Answer:
The target is 2 meters ahead of you.
If you throw the snowball with a velocity S, then the time that the snowball will need to hit the target is:
2m/S = T
Now let's analyze the vertical problem.
The only force acting on the snowball is the gravitational force, then the acceleration will be -g = -9.8m/s^2.
a(t) = -9.8m/s^2
For the vertical velocity, we need to integrate over time and get:
v(t) = (-9.8m/s^2)*t + v0
Where v0 is the initial vertical velocity, in this case is zero because the ball is thrown horizontally.
v(t) = (-9.8m/s^2)*t
For the vertical position, we integrate again over time.
p(t) = (-4.9m/s^2)*t^2 + p0.
Now, we know that when the ball hit the target, it hits 9 meters below the desired point (where the desired point is p0), so p(2m/S) = p0 - 9m.
Then we have:
(-4.9m/s^2)*(2m/S)^2 = -9m.
We need to solve this for S.
(-4.9m/s^2)*4m^2/-9m = S^2
2.178 m^2/s^2 = S^2
√(2.178 m^2/s^2) = S = 1.48 m/s
The horizontal velocity is 1.48 m/s
