Answer:
(a) R = 1Ω
(b) τ = 3
Explanation:
The time constants of the given circuits are as follows

If the two circuits have equal time constants, then

Therefore, the time constant in any of the circuits is

Answer:
∆h = 0.071 m
Explanation:
I rename angle (θ) = angle(α)
First we are going to write two important equations to solve this problem :
Vy(t) and y(t)
We start by decomposing the speed in the direction ''y''


Vy in this problem will follow this equation =

where g is the gravity acceleration

This is equation (1)
For Y(t) :

We suppose yi = 0

This is equation (2)
We need the time in which Vy = 0 m/s so we use (1)

So in t = 0.675 s → Vy = 0. Now we calculate the y in which this happen using (2)

2.236 m is the maximum height from the shell (in which Vy=0 m/s)
Let's calculate now the height for t = 0.555 s

The height asked is
∆h = 2.236 m - 2.165 m = 0.071 m
The work done to push the box is equal to the product between the force and the distance through which the force is applied:

In our problem, the force is F=1.4 N and the distance covered is d=150 m, so the work done by pushing the box is
M1U1 + M2V2 = (M1+M2)V, where M1 is the mass of the moving car, M2 is the mass of the stationary car, U1 is the initial velocity, and V is the common velocity after collision.
therefore;
(1060× 16) + (1830 ×0) = (1060 +1830) V
16960 = 2890 V
V = 5.869 m/s
The velocity of the cars after collision will be 5.689 m/s
By using the Plancks-Einstein equation, we can find the energy;
E = hf
where h is the plancks constant = 6.63 x 10⁻³⁴
f = frequency = 3.55 x 10¹⁷hz
E = (6.63 x 10⁻³⁴) x (3.55 x 10¹⁷)
E = 2.354 x 10⁻¹⁶J