You are driving up a long, inclined road. After 1.50mi you notice that signs along the roadside indicate that your elevation has increased by 510ft . b) How far do you have to drive to gain an additional 110ft of elevation

1.825 miles

Explanation:

Given that :

Distance driven = hypotenus = 1.5 miles

Elevation at distance of 1.5 miles = 510 feets

Converting miles to feets for the hypotenus :

1 mile = 5280 feets

1.5 miles = (5280 * 1.5) = 7920 feets

To obtain the angle of inclination :

Using Pythagoras rule :

Sinθ = opposite / hypotenus

θ = Sin^-1(510 / 7920)

θ = 3.692°

For an additional elevation of 110 ft ; new height = 110 + 510 = 620 feets

Distance driven, d =?

Sin 3.69 = (620 / d)

0.0643581 * d = 620

d = 620 / 0.0643581

d = 9633.5970 feets

Converting to feets :

9633.5970 / 5280 = 1.8245448

= 1.825 miles

Answer:

Step-by-step explanation:

To solve this problem, we can use the conservation of energy and conservation of momentum principles.

Conservation of energy:

The total initial energy is the rest energy of the proton and neutron, which is given by:

Ei = (mp + mn)c^2

where mp and mn are the masses of the proton and neutron, respectively, and c is the speed of light.

The total final energy is the rest energy of the deuteron plus the energy of the gamma ray, which is given by:

Ef = (md)c^2 + Eg

where md is the mass of the deuteron and Eg is the energy of the gamma ray.

According to the conservation of energy principle, the initial energy and final energy must be equal, so we have:

Ei = Ef

(mp + mn)c^2 = (md)c^2 + Eg

Conservation of momentum:

The total initial momentum is zero because the proton and neutron are at rest. The total final momentum is the momentum of the deuteron and the momentum of the gamma ray. Since the gamma ray is massless, its momentum is given by:

pg = Eg/c

where pg is the momentum of the gamma ray.

According to the conservation of momentum principle, the total final momentum must be equal to zero, so we have:

0 = pd + pg

where pd is the momentum of the deuteron.

Solving for md and pd:

From the conservation of energy equation, we can solve for md:

md = (mp + mn - Eg/c^2)/c^2

Substituting this expression into the conservation of momentum equation, we get:

pd = -pg = -Eg/c

Substituting the given values, we have:

mp = 1.6726 × 10^-27 kg mn = 1.6749 × 10^-27 kg Eg = 2.2 × 10^6 eV = 3.52 × 10^-13 J

Using c = 2.998 × 10^8 m/s, we get:

md = (1.6726 × 10^-27 kg + 1.6749 × 10^-27 kg - 3.52 × 10^-13 J/(2.998 × 10^8 m/s)^2)/(2.998 × 10^8 m/s)^2 = 3.3435 × 10^-27 kg

pd = -Eg/c = -(3.52 × 10^-13 J)/(2.998 × 10^8 m/s) = -1.1723 × 10^-21 kg·m/s

Therefore, the mass of the deuteron is 3.3435 × 10^-27 kg, and its momentum is -1.1723 × 10^-21 kg·m/s.

Answer:

Step-by-step explanation:

Time taken by the tomatoes to each the ground

using h = 1/2 g t^2 

t^2 = 2h/g = 2 x 50/ 9.8 = 10.2

t = 3.2 sec 

horizontal ditance = speed x time = 3 x 3.2 = 9.6 meters

The question specifies the diameter of the screw, therefore the IMA of this screw is 0.812? / 0.318 = 8.02