Answer:
v = -14 m/s
Explanation:
Given that,
Initial location of the ball, X₁ = 10 m
Final position of the ball, X₂ = -25 m
Time taken to travel is, t = 2.5 s
The average velocity of the ball is given by the formula,
V = X₂ - X₁ / t m/s
Substituting the values in the above equation,
V = -25 - 10 / 2.5
= -14 m/s
The negative sign in the velocity indicates that ball rolls in the opposite direction.
Hence, the average velocity of the ball is v = -14 m/s
Answer:
d = 11.1 m
Explanation:
Since the inclined plane is frictionless, this is just a simple application of the conservation law of energy:

Let d be the displacement along the inclined plane. Note that the height h in terms of d and the angle is as follows:

Plugging this into the energy conservation equation and cancelling m, we get

Solving for d,

this is basically the same as volume, no?
So, 5.345*4.128*3.859=85.145
Answer:
The resistance of the inductor at resonance is 258.76 ohms.
Explanation:
Given;
resistance of the resistor, R = 305 ohm
capacitance of the capacitor, C = 1.1 μF = 1.1 x 10⁻⁶ F
inductance of the inductor, L = 42 mH = 42 x 10⁻³ H = 0.042 H
At resonance the inductive reactance is equal to capacitive reactance.

Where;
F₀ is the resonance frequency

The inductive reactance is given by;

Therefore, the resistance of the inductor at resonance is 258.76 ohms.