A 200-lb object is released from rest 600 ft above the ground and allowed to fall under the influence of gravity. Assuming that the force in pounds due to air resistance is minus10v, where v is the velocity of the object in ft/sec, determine the equation of motion of the object. When will the object hit the ground? Assume that the acceleration due to gravity is 32 ft divided by sec squared and let x(t) represent the distance the object has fallen in t seconds.

x(t) = 20t + 12.75e⁻¹•⁶ᵗ + 487.5

t = 24.375 s

Explanation:

The force balance on the object is given as

Net force = W - Drag force

ma = W - 10v

a = (dv/dt)

ma = m(dv/dt) = 200 - 10v

W = mg

200 = m×32

m = 6.25 kg

m(dv/dt) = 200 - 10v

6.25(dv/dt) = 200 - 10v

(dv/dt) = 32 - 1.6v

v' + 1.6v = 32

Solving this differential equation using the integrating factor method

(ve¹•⁶ᵗ) = ∫ (32e¹•⁶ᵗ) dt

ve¹•⁶ᵗ = (20e¹•⁶ᵗ) + c (where c = constant of integration)

v = (20 + ce⁻¹•⁶ᵗ)

At t = 0, v = 0

0 = 20 + c

c = -20

v = (20 - 20e⁻¹•⁶ᵗ)

v = (dx/dt)

(dx/dt) = 20 - 20e⁻¹•⁶ᵗ

dx = (20 - 20e⁻¹•⁶ᵗ) dt

x(t) = 20t + 12.5e⁻¹•⁶ᵗ + c (c is still the constant of integration)

At t = 0, x = - 500

- 500 = 0 + 12.5 + c

c = 512.5

x(t) = 20t + 12.75e⁻¹•⁶ᵗ - 487.5

when the object hits the ground, x = 0

0 = 20t + 12.75e⁻¹•⁶ᵗ - 487.5

20t + 12.75e⁻¹•⁶ᵗ = 487.5

Solving by trial and error,

t = 24.375 s

Hope this Helps!!!

electromagnetic shielding is the practice of reducing the electromagnetic field in a space by blocking the field with barriers made of conductive or magnetic materials. shielding is typically applied to enclosures to isolate electrical devices from their surroundings, and to cables to isolate wires from the environment through which the cable runs. electromagnetic shielding that blocks radio frequency electromagnetic radiation is also known as rf shielding.

the shielding can reduce the coupling of radio waves, electromagnetic fields and electrostatic fields. a conductive enclosure used to block electrostatic fields is also known as a faraday cage. the amount of reduction depends very much upon the material used, its thickness, the size of the shielded volume and the frequency of the fields of interest and the size, shape and orientation of apertures in a shield to an incident electromagnetic

from wikipedia

54 degrees incident angle = reflected angle

angle is from normal turned to line of ray