The half-life equation 
in which <em>n </em>is equal to the number of half-lives that have passed can be altered to solve for <em>n.</em>
<em>
</em>
<em>
</em>
Then, the number of half-lives that passed can be multiplied by the length of a half-life to find the total time.
<em>2 * 5700 = </em>11400 yr
Answer:
The initial velocity of the water from the tank is 5.42 m/s
Explanation:
By applying Bernoulli equation between point 1 and 2
At the point 1
P₁=0 ( Gauge pressure)
V₁= 0 m/s
Z₁=3 m
At point 2
P₂=0 ( Gauge pressure)
Z₂= 0 m/s
Now by putting the values
V₂= 5.42 m/s
The initial velocity of the water from the tank is 5.42 m/s
Answer:
26.67 m/s
Explanation:
From the law of conservation of linear momentum, the initial sum of momentum equals the final sum.
p=mv where p is momentum, m is the mass of object and v is the speed of the object
Initial momentum
The initial momentum will be that of basketball and volleyball, Since basketball is initially at rest, its initial velocity is zero
Final momentum
This can be calculated with the law of conservation of energy. The sky lift is starting with the speed v= 15.5 m/s and all of it's kinetic energy Ek is transformed to potential energy Ep so the energies have to be equal: Ep=Ek.
Since Ek=(1/2)*m*v² where m is mass and v is the speed, Ep=m*g*h, where m is mass, g= 9.81 m/s² and h is height. Now:
Ek=Ep
(1/2)*m*v²=m*g*h, masses cancel out,
(1/2)*v²=g*h, divide by g to get the height,
(1/2*g)*v²=h and now plug in the numbers:
h=12.245 m. Height of the hill rounded to the nearest tenth is h=12.25 m
Complete question:
The classic Goodyear blimp is essentially a helium balloon— a big one, containing 5700 m³ of helium. If the envelope and gondola have a total mass of 4300 kg, what is the maximum cargo load when the blimp flies at a sea-level location? Assume an air temperature of 20°C.
Answer:
52.4 kN
Explanation:
The helium at 20°C has a density of 0.183 kg/m³, and the cargo load is the weight of the system, which consists of the envelope, the gondola, and the helium.
The helium mass is the volume multiplied by the density, thus:
mHe = 5700 * 0.183 = 1043.1 kg
The total mass is then 5343.1 kg. The weight is the mass multiplied by the gravity acceleration (9.8 m/s²), so:
W = 5343.1*9.8
W = 53362.38 N
W = 52.4 kN
