1. A four-lane freeway (two lanes in each direction) is located on rolling terrain and has 12-ft lanes, no lateral obstructions

Answer:

Change in length = 0.0913 in

Explanation:

Given data:

Length = 6 ft

Diameter = 0.2 in

Load w = 200 lb/ft

Solution:

We start by applying the equilibrium moment about point C, expressed as

∑M(c) = 0.............1

This can be used to find the force in AB.

10× 200 × ( 5) - (T cos(30)) × 10 = 0

Solving gives us

Tension in wire T(AB) = 1154.7 lb

We also know the modulus of elasticity for A992 is

E = 29000 ksi

And the area will be

Area =

The change in length is expressed as

Change in length = .........2

Substituting values results in

Change in length =

Change in length = 0.0913 in

Answer:

Refer to the attached document

1512 ft

Explanation:

Because the acceleration is constant or zero, the acceleration-time graph consists of horizontal segments. The values for t2 and a4 are derived as follows:

Acceleration - Time

0 < t < 6: Velocity change = area beneath the a–t graph

V_6 - 0 =  (6 s)(4 ft/s²) = 24 ft/s

6 < t < t2: The velocity rises from 24 to 48 ft/s,

Velocity change = area beneath the a–t graph

48 - 24 = (t2 - 6) * 6

t2 = 10 s

t2 < t < 34: The velocity remains constant, meaning acceleration is zero.

34 < t < 40: Velocity change = area beneath the a–t graph

0 - 42 = 6*a4

a4 = - 8 ft / s²

A negative acceleration shows the area lies below the t-axis, indicating a decrease in speed.

Velocity - Time

Since acceleration remains constant or zero, the v−t graph is made up of linear segments connecting the calculated points.

Position change = area beneath the v−t graph

0 < t < 6:  x6 - 0 = 0.5*6*24 = 72 ft

6 < t < 10:    x10 - x6 = 0.5*4*(24 + 48) = 144 ft

10 < t < 34: x34 - x10 = 48*24 = 1152 ft

34 < t < 40: x40 - x34 = 0.5*6*48 = 144 ft

Summing these position changes yields the distance from A to B:

d = x40 - 0 = 1512 ft

Answer:

The calculated result is 11.7 ft

Explanation:

You can apply the combined gas law, which incorporates Boyle's law, Charles's law, and Gay-Lussac's Law, because hydrogen demonstrates ideal gas behavior under these specific conditions.

where the subscripts indicate "p" for pressure, "V" for volume, and "T" for temperature (in Kelvin) at varying moments. Let's denote as the balloon at 150,000 ft so

and .

Then represents the point at which the balloon is on the ground.

and .

Based on the first equation

, we find

and consequently the radius turns out to be

.