Distance traveled by the rocket= 1002 m
Explanation:
initial velocity= Vi=0
final velocity= V=445 m/s
time=4.5 s
Acceleration=a=99 m/s²
using kinematic equation
h= Vi t + 1/2 at²
h= 0(4.5) + 1/2 (99) (4.5)²
h=1002 m
Thus the distance traveled by the rocket= 1002 m
Answer:
1. k = 183.33 N/m
2. E = 0.33 J
3. x(t) = 0.06cos(2πt)
Explanation:
1. Determine the spring constant of the spring.
To determine the spring constant, we use hooke's law:
F = kΔx
where
F is the force = 11 N
Δx is the displacement = 0.06 m
k is the spring constant
k = F/Δx
k = 11/0.06 = 183.33 N/m
2. Determine the total energy of the system
the total energy(E) = Δ = 0.5 × 183.33 × 0.06² = 0.33 J.
Therefore the total energy of the system is 0.33 J
3. Write an expression x(t) for the motion of the cart. Assume the frequency f=1Hz. Express your answer in terms of the variable t and constant pi.
The expression for the motion of the cart x(t) is given by:
x(t) = Δxcos(2πft)
where the frequency f = 1 Hz
x(t) = 0.06cos(2π ×1 × t)
x(t) = 0.06cos(2πt)
C. 0.37V. A capacitor of 650x10⁻⁴F that stores 24x10⁻³C has a potential difference of 0.37V between its plates.
The key to solve this problem is using the capacitance equation C = Q/Vᵃᵇ, where C is the capacitance, Q the charge stored in the plates, and Vᵃᵇ the potential difference between the plates.
A 650x10⁻⁴F capacitor stores 24x10⁻³C, clear Vᵃᵇ for the equation:
C = Q/Vᵃᵇ -----------> Vᵃᵇ = Q/C
Solving
Vᵃᵇ = 24x10⁻³C/650x10⁻⁴F = 0.37V
The answer is D: All of the above.