Answer:
9155 years old
Explanation:
We use the following expression for the decay of a substance:
So we first estimate the value of k knowing that the half-life of the C14 is 5730 years:
so, now we can estimate the age of the artifact by solving for"t" in the equation:
which we can round to 9155 years old.
Answer: 0.01 m
Explanation: The formulae for capillarity rise or fall is given below as
h = (2T×cosθ)/rpg
Where θ = angle mercury made with glass = 50°
T = surface tension = 0.51 N/m
g = acceleration due gravity = 9.8 m/s²
r = radius of tube = 0.5mm = 0.0005m
p = density of mercury.
h = height of rise or fall
From the question, specific gravity of density = 13.3
Where specific gravity = density of mercury/ density of water, where density of water = 1000 kg/m³
Hence density of mercury = 13.3×1000 = 13,300 kg/m³.
By substituting parameters, we have that
h = 2×0.51×cos 50/0.0005×9.8×13,300
h = 0.6556/65.17
h = 0.01 m
Work done = force * distance moved (in direction of the force)
force= mass* acceleration
force=58.1N
58.1*(5.8*10^4)
=3,369,800 J
<span>31.3 m/s
Since the water balloon is being launched at a 45 degree angle, the horizontal and vertical speeds will be identical. Also the time the balloon takes to reach its peak altitude will match the time it takes to fall. So let's create a few expressions about what we know.
Distance the water balloon travels at velocity v for time t
d = vt
Total time required for the entire trip is double since the balloon goes up, then goes down
t = 2v/a
Now let's plug in the numbers we have, assuming the acceleration due to gravity is 9.8 m/s^2
t = 2v/9.8
100 = vt
Substitute 2v/9.8 for t in the 2nd formula
100 = v(2v/9.8)
Solve for v.
100 = v(2v/9.8)
100 = 2v^2/9.8
980. = 2v^2
490 = v^2
22.13594 = v
So we now know that both the horizontal velocity and vertical velocity needed is 22.13594 m/s. Let's verify that
2*22.13594 / 9.8 = 4.51754
So it will take 4.51754 second for the balloon to hit the ground after being launched.
4.51754 * 22.13594 = 100
And during that time it will travel 100 meters horizontally.
But we need to know the total velocity. And the Pythagorean theorem comes to the rescue. Just square the 2 velocities, add them together, and take the square root. We already know the square is 490 from the work above, so
sqrt(490+490) = sqrt(980) = 31.30495 m/s</span>
Answer:
1.43 s
Explanation:
The time it takes for the container to reach the ground is determined only by the vertical motion of the container, which is a free-fall motion, so a uniformly accelerated motion with a constant acceleration of g=9.8 m/s^2 towards the ground.
The vertical distance covered by an object in free fall is given by
where
u = 0 is the initial vertical speed
t is the time
a= g = 9.8 m/s^2 is the acceleration
since u=0, it can be rewritten as
And substituting S=10.0 m, we can solve for t, to find the duration of the fall:
