Answer:
Average speed, v = 1.66 km/h
Explanation:
It is given that, Ian walks 2 km to his best friend’s house, then walks 0.5 km to the library. He then makes a 2.5 km walk home.
Total time taken in the entire walk, t = 3 hours
We need to find the average speed of the Ian during his journey.
Total distance covered is,
Average velocity,
So, the average speed during the entire journey is 1.66 km/h. Hence, this is the required solution.
Answer:
Zero
Explanation:
here, the inductive reactance and the capacitive reactance is same, so this is the condition for resonance.
In the condition for resonance,
the circuit and the voltage in the circuit is in the same phase and the impedance of the circuit is minimum which is equal to the resistance of the circuit.
The phase angle is given by
Ф = 0
Answer:
a) x = v₀ₓ t
, y = t - ½ g t²
Explanation:
This is a projectile launch problem, let's use Newton's second law on each axis
X axis
F = m a
Since there is no acceleration on the x axis, the force on this axis is zero
Y Axis
-W = m
-m g = m
= -g
In this axis the acceleration is the acceleration of gravity
Now we can use science to find the position of the body on each axis
X axis
x = v₀ₓ t + ½ a t²
As the acceleration on this axis is zero
x = v₀ₓ t
Y Axis
y = t + ½
t²
The acceleration on this axis is –g
y = t - ½ g t²
B) to find the maximum value of distance r
r =√ x² + y²
r = √( v₀ₓ² t² + ( t + ½ g t²)²
We can find the maximum value of r using time respect derivatives
dr / dt = 0
0 = ½ 1/√( v₀ₓ² t² + ( t + ½ g t²)² (v₀ₓ² 2t + 2 (
t - ½ g t²)(
- ½ g2t)
We simplify this expression
0 = v₀ₓ² 2t + 2 ( t - ½ g t²) (
- ½ g2t)
-v₀ₓ² t =( t - ½ g t²) (
- ½ g2t)
-v₀ₓ² t = ² t -3/2 gt²
+ 1/2 g² t³
½ g² t²- 3/2 g t =
² + v₀ₓ²
Let's use trigonometry to find go and vox
sin θ = / v₀
cos θ = vox / v₀
= v₀ sin θ
v₀ₓ = v₀ cos θ
We replace
½ g² t² -3/2 g t = v₀ (sin² θ + cos² θ)
g t² - 3v₀ sin θ t = 2 v₀/g
The time is maximum for the angle is zero