
The velocity at time
is

Take two vectors that point in the positive
and positive
directions, such as
and
. The dot products of the velocity vector with
and
are

and

We want the angles between these vectors to be 45º, for which we have
. So



When
, the velocity vector is equal to the zero vector, which technically has no direction/doesn't make an angle with any other vector. So the only time this happens is for

Answer:
v₂ = 15.24 m / s
Explanation:
This is an exercise in fluid mechanics
Let's write Bernoulli's equation, where the subscript 1 is for the factory pipe and the subscript 2 is for the tank.
P₁ + ½ ρ v₁² + ρ g y₁ = P₂ + ½ ρ v₂² + ρ g y₂
They indicate the pressure in the factory P₁ = 140000 Pa, the velocity
v₁ = 5.5 m / s and the initial height is zero y₁ = 0
the tank is at a pressure of P2 = 2000 Pa and a height of y₂ = 6.0 m
P₁ -P₂ + ρ g (y₁ -y₂) + ½ ρ v₁² = ½ ρ v₂²
let's calculate
140,000 - 2000 + ρ 9.8 (0- 6) + ½ ρ 5.5² = ½ ρ v₂²
138000 - ρ 58.8 + ρ 15.125 = ½ ρ v2²
v₂² = 2 (138000 /ρ - 58.8 + 15.125)
v₂ =
In the exercise they do not indicate what type of liquid is being used, suppose it is water with
ρ = 1000 kg / m³
v₂ =
v₂ = 15.24 m / s
Answer:
10 s
Explanation:
Given:
Δx = 100 m
v₀ = 0 m/s
a = 2 m/s²
Find: t
Δx = v₀ t + ½ at²
100 m = (0 m/s) t + ½ (2 m/s²) t²
t = 10 s
400 horsepower is produced by 2023 z's 3. 0-liter twin-turbo 6-cylinder engine.
<h3>What is horsepower?</h3>
The power an engine produced is referred to as horsepower. In the British Imperial System, one horsepower equals 33,000 foot-pounds of work per minute, i.e., the force required to lift a mass of 33,000 pounds off the ground in a single motion for one minute.
The new Z's 3.0-liter twin-turbo V6 engine produces 400 horsepower and 350 pound-feet of torque. This is 68 horsepower and 80 lb-ft more than the previous 370Z. The 6-speed manual transmission that comes standard or the optional 9-speed automatic transmission with paddle shifters are both paired with this one engine option.
Learn more about horsepower here:
brainly.com/question/17918928
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Answer:
2666.7 N/m
Explanation:
Spring constant = force / displacement
k = F / x
k = 400 N / 0.15 m
k = 2666.7 N/m