Answer:
The fluids speed at a)
and b)
are
and
respectively
c) Th volume of water the pipe discharges is:
Explanation:
To solve a) and b) we should use flow continuity for ideal fluids:
(1)
With Q the flux of water, but Q is
using this on (1) we have:
(2)
With A the cross sectional areas and v the velocities of the fluid.
a) Here, we use that point 2 has a cross-sectional area equal to
, so now we can solve (2) for
:

b) Here we use point 2 as
:

c) Here we need to know that in this case the flow is the volume of water that passes a cross-sectional area per unit time, this is
, so we can write:
, solving for V:

Answer:
d.
Explanation:
Since the dart's initial speed v at angle has both vertical and horizontal components v₀sinθ and v₀cosθ respectively, the vertical component of the speed continues to decrease until it hits the target. It's displacement ,s is gotten from
s = y - y₀ = (v₀sinθ)t - 1/2gt² where y₀ = 0 m
y - 0 = (v₀sinθ)t - 1/2gt²
y = (v₀sinθ)t - 1/2gt²
which is the parabolic equation for the displacement of the dart.
Note that the horizontal component of the dart's velocity does not change during its motion.
Since the target falls vertically, with initial velocity u = 0 (since it was stationary before the string cut), it's displacement ,s' is gotten from
s' = y - y₀' = ut - 1/2gt² where y₀' = initial height of target above the ground
= (0 m/s)t - 1/2gt²
= 0 - 1/2gt²
y - y₀' = - 1/2gt²
y = y₀' - 1/2gt²
which is the parabolic equation for the displacement of the target.
The equation for both the displacement of the dart and the target can only be gotten if we considered vertical motion. So, the displacement component of both the dart and target are both vertical.
So, the answer is d.
I believe the answer is D
Hope this helps :)