Answer:
v = 5.7554 m/s
Explanation:
First of all we need to know if the angle of the vine is measured in the horizontal or vertical.
To do this easier, let's assume the angle is measured with the horizontal. In this case, the innitial height of the monkey will be:
h₀ = h sinα
h₀ = 5.32 sin43° = 3.6282 m
As the monkey is dropping from the innitial point which is the suspension point, is also dropping from 5.32. Then the actual height of the monkey will be:
Δh = 5.32 - 3.63 = 1.69 m
In order to calculate the speed of the monkey we need to understand that the monkey has a potential energy. This energy, because of the gravity, is converted in kinetic energy, and the value will be the same. Therefore we can say that:
Ep = Ek
From here, we can calculate the speed of the monkey.
Ep = mgΔH
Ek = 1/2 mv²
The potential energy is:
Ep = 16.9 * 9.8 * 1.69 = 279.9
Now with the kinetic energy:
1/2 * (16.9) * v² = 279.9
v² = (279.9) * 2 / 16.9
v² = 33.12
v = √33.12
<h2>
v = 5.7554 m/s</h2>
Hope this helps
<u>Answer:</u> The mass of the second car is 12666.7 kg
<u>Explanation:</u>
To calculate the mass of car, we use the equation of law of conservation of momentum, which is:

where,
= mass of car 1 = 9500 kg
= Initial velocity of car 1 = 14 m/s
= mass of car 2 = ? kg
= Initial velocity of car 2 = 0 m/s
= Final velocity = 6.0 m/s
Putting values in above equation, we get:

Hence, the mass of the second car is 12666.7 kg
Answer:
The correct answer is "53.15 days".
Explanation:
Given that:
Half life of
,

- Let the initial activity be "
". - and, activity to time t be "R".
To find t when R will be "1%" of
, then
⇒ 
As we know,
⇒ 
or,
∴ 
By putting the values, we get


We know that,
Decay constant, 
hence,
⇒ 


Answer:
water is in the vapor state,
Explanation:
We must use calorimetry equations to find the final water temperatures. We assume that all energy is transformed into heat
E = Q₁ + 
Where Q1 is the heat required to bring water from the current temperature to the boiling point
Q₁ = m
(
-T₀)
Q₁ = 50 4180 (100 - 37)
Q₁ = 1.317 10⁷ J
Let's calculate the energy so that all the water changes state
= m L
= 50 2,256 106
= 1,128 10⁸ J
Let's look for the energy needed to convert all the water into steam is
Qt = Q₁ +
Qt = 1.317 107 + 11.28 107
Qt = 12,597 10⁷ J
Let's calculate how much energy is left to heat the water vapor
ΔE = E - Qt
ΔE = 10¹⁰ - 12,597 10⁷
ΔE = 1000 107 - 12,597 107
ΔE = 987.4 10⁷ J
With this energy we heat the steam, clear the final temperature
Q = ΔE = m
(
-To)
(
-T₀) = ΔE / m 
= T₀ + ΔE / m 
= 100 + 987.4 10⁷ / (50 1970)
= 100 + 1,002 10⁵
= 1,003 10⁵ ° C
This result indicates that the water is in the vapor state, in realizing at this temperature the water will be dissociated into its hydrogen and oxygen components