a) 0.13*τ; b) 2.08*τ. To describe the discharging process of a capacitor through a resistor, consider the following: Q(t) = Qo * exp(-t/τ) to signify a loss of 1/8 of its charge. In this scenario, Q(t) = 7/8 * Qo = 7/8 * exp(-t/τ). By rearranging, we have ln(7/8)*τ = -t, thus t = -ln(7/8)*τ = 0.13. For a loss of 7/8 of its charge, we use Q(t) = 1/7 * Qo * exp(-t/τ), leading to t = -ln(1/8)*τ = 2.08.
Answer: SG = 2.67
The specific gravity for the sand is 2.67
Explanation:
Specific gravity is determined by the formula: density of the substance/density of water
Provided information;
Mass of sand m = 100g
The volume of sand equals the volume of water it displaces
Vs = 537.5cm^3 - 500 cm^3
Vs = 37.5cm^3
Calculating density of sand = m/Vs = 100g/37.5 cm^3
Ds = 2.67g/cm^3
Density of water Dw = 1.00 g/cm^3
Thus, the specific gravity of the sand can be expressed as
SG = Ds/Dw
SG = (2.67g/cm^3)/(1.00g/cm^3)
SG = 2.67
The specific gravity of the sand stands at 2.67
Answer:

Explanation:
We start with the fact that
Initially, the spacecraft was at rest, u = 0
The final velocity of the rocket is given as v = 11 m/s
The distance that the rocket covers during acceleration is given as d = 213 m
We seek to determine the acceleration that the occupants of the spacecraft experience during launch, which is derived from the principles of kinematics. By applying the
third motion equation we can find the acceleration.

Thus, the acceleration felt by those inside the spacecraft is
.
Speed is defined as distance over time. Hence, to determine the distance, we use d = V * t. Plugging in the values yields d = (72 Km / h) * (1h / 3600s) * (4.0 s) = 0.08Km. Thus, during this distracted period, a distance of 0.08Km was covered.
Answer:
2.57 hours
Explanation:
Let t (in hours) represent the time it takes for Elsie to walk until they are separated by 25 miles. Since Steve starts 2 hours earlier, his time will be t + 2.
The distance covered by Steve heading north is 
The distance Elsie travels heading west is 
The separation between Steve and Elsie is

We can solve for t by squaring both sides.







Therefore, t = 2.57 or t = -4.13.
Since t cannot be negative, we select t = 2.57 hours.