Answer:
2 secs; 65 feet
Explanation:
The function guiding the water bottle is given as:
f(x) = -16t² + 64t + 1
The bottle will reach maximum height when velocity, df/dt (velocity is the first derivative of distance) = 0.
Therefore:
df/dt = 0 = -32t + 64
=> 32t = 64
t = 64/32 = 2 seconds
This is the time it will take to reach the maximum height.
To find this height, we insert t = 2 into the function f(x):
f = -16(2)² + 64(2) + 1
f = -(16 * 4) + 128 + 1
f = -64 + 128 + 1
f = 65 ft
Its maximum height is 65 ft.
Answer:
the object will not return to the original position because it will not have any forces helping it to go up the hill
the center of mass falls since it is going downwards
Hope this helps!! have a great day
Explanation:
Answer:
A. Z = 185.87Ω
B. I = 0.16A
C. V = 1mV
D. VL = 68.8V
E. Ф = 30.59°
Explanation:
A. The impedance of a RL circuit is given by the following formula:
(1)
R: resistance of the circuit = 160-Ω
w: angular frequency = 220 rad/s
L: inductance of the circuit = 0.430H
You replace in the equation (1):

The impedance of the circuit is 185.87Ω
B. The current amplitude is:
(2)
V: voltage amplitude = 30.0V

The current amplitude is 0.16A
C. The current I is the same for each component of the circuit. Then, the voltage in the resistor is:
(3)
D. The voltage across the inductor is:

E. The phase difference is given by:

<h3>a. The impulse</h3>
The impulse is 100.0 Ns
The impulse I = Ft where
- F =average force = 50.0 N and
- t = time = 2.0 s
Substituting these values into the equation, we have
I = Ft
I = 50.0 N × 2.0 s
I = 100.0 Ns
The impulse is 100.0 Ns
<h3>b. Change in momentum</h3>
The change in momentum is 100 kgm/s
Since change in momentum Δp = I where I = impulse.
Since I = 100.0 Ns,
Substituting this into the equation, we have
Δp = I
= 100.0 Ns
= 100 kgm/s
The change in momentum is 100 kgm/s
<h3>c. Mass's change in velocity</h3>
The change in velocity is 25.0 m/s
Since change in momentum Δp = mΔv where
- m = mass = 4.0 kg and
- Δv = change in velocity.
Making Δv subject of the formula, we have
Δv = Δp/m
Substituting the values of the variables into the equation, we have
Δv = Δp/m
Δv = 100.0 kgm/s/4.0 kg
Δv = 25.0 m/s
The change in velocity is 25.0 m/s
Learn more about impulse here:
brainly.com/question/25700778