Answer:
a) a = - 0.0833 m / s², b) t = 4.4 s
Explanation:
a) this is a kinematics exercise where the acceleration is along the inclined plane
v = v₀ - a t
a = v₀ - v / t
a = 3 - 8/60
a = - 0.0833 m / s²
b) in this case the final velocity is zero
v = v₀ - a t
0 = v₀ - at
t = v₀ / a
t = 28 / 6.4
t = 4.375 s
t = 4.4 s
High school???
No way
It's work.
Explanation:
It is given that,
Velocity of the electron, 
Magnetic field, 
Charge of electron, 
(a) Let 
is the force on the electron due to the magnetic field. The magnetic force acting on it is given by :
![F_e=1.6\times 10^{-19}\times [(2\times 10^6i+3\times 10^6j)\times (0.030i-0.15j)]](https://tex.z-dn.net/?f=F_e%3D1.6%5Ctimes%2010%5E%7B-19%7D%5Ctimes%20%5B%282%5Ctimes%2010%5E6i%2B3%5Ctimes%2010%5E6j%29%5Ctimes%20%280.030i-0.15j%29%5D)
(b) The charge of electron, 
The force acting on the proton is same as force on electron but in opposite direction i.e (-k). Hence, this is the required solution.
let Coefficients of Friction of Rubber on asphalt (dry) =0.7
F= Coefficients of Friction * normal force = 0.7 * 60 =42 N
so the net force of the rubber is zero, meaning it will travel at a constant speed.
When the rubber is travel at 2m/s, 42N is required to keep moving at constant speed
Let us say that x is the cut that we will make on the
sides to make a box, therefore the new dimensions are:
l = 15 – 2x
w = 8 – 2x
It is 2x since we cut on two sides.
We know that volume is:
V = l w x
V = (15 – 2x) (8 – 2x) x
V = 120x – 30x^2 – 16x^2 + 4x^3
V = 120x – 46x^2 + 4x^3
Taking the 1st derivative:
dV/dx = 120 – 92x + 12x^2
Set dV/dx = 0 to get maxima:
120 – 92x + 12x^2 = 0
Divide by 12:
x^2 – (92/12)x + 10 = 0
(x – (92/24))^2 = -10 + (92/24)^2
x - 92/24 = ±2.17
x = 1.66, 6
We cannot have x = 6 because that will make our w
negative, so:
x = 1.66 inches
So the largest volume is:
V = 120x – 46x^2 + 4x^3
V = 120(1.66) – 46(1.66)^2 + 4(1.66)^3
V = 90.74 cubic inches
