Answer:
Momentum of object A = Momentum of object C < momentum of B.
Explanation:
The momentum of an object is equal to the product of mass and velocity.
Object A has a mass m and a speed v. Its momentum is :
p = mv
Object B has a mass m/2 and a speed 4v. Its momentum is :
p = (m/2)×4v = 2mv
Object C has a mass 3m and a speed v/3. Its momentum is :
p = (3m)×(v/3) = mv
So,
Momentum of object A = Momentum of object C < momentum of B.
B. 8540, (assuming you meant 8.54 x 10 to the power 3) you move the decimal point 3 places to the right, if the decimal point can't pass any more numbers add zeros. If it confuses you to think of it this way do 10 cubed first, i.e. 10 x 10 x10 = 1000 and then do 8.54 x 1000 if thats easier for you.
The equation relevant to this is:
S(t) = So + Vot - At²/2 <span>
</span>
<span>Therefore
we can create two equations:
<span>S(t) = 90 = So - 4t - 16.1t² -->
eqtn 1</span>
<span>S(t+2) = 10 = So - 4(t+2) - 16.1(t+2)² --> eqtn 2</span>
</span>
<span>Expanding
eqtn 2:
10 = So - 4t - 8 - 16.1(t² + 4t + 4)
10 = So - 4t - 8 - 16.1t² - 64.4t - 64.4
10 + 8 + 64.4 = So - 68.4t - 16.1t²
<span>82.4 = So - 68.4t - 16.1t² -->
eqtn 3</span></span>
<span>
Subtracting eqtn 1 by eqtn 3:</span>
90 = So - 4t - 16.1t²
82.4 = So - 68.4t - 16.1t²
=> 7.6 = 64.4t
t = 0.118 s
Therefore calculating for initial height So:<span>
<span>82.4 = So - 68.4(0.118) - 16.1(0.118)²
<span>So = 90.7 ft</span></span></span>
Answer:
1. 1800 W
2. $ 17.3
Explanation:
From the question given above, the following data were obtained:
Current (I) = 15 A
Voltage (V) = 120 V
Time (t) = 20 h per day
Duration = 31 days
Cost = 15.5 cents per kWh
1. Determination of the power.
Current (I) = 15 A
Voltage (V) = 120 V
Power (P) =?
P = IV
P = 15 × 120
P = 1800 W
Thus, 1800 W of power is required.
2. Determination of the cost per month (31 days).
We'll begin by converting 1800 W to KW.
1000 W = 1 KW
Therefore,
1800 W = 1800 W × 1 KW / 1000 W
1800 W = 1.8 KW
Next, we shall determine the energy consumption for 31 days. This can be obtained as follow:
Power (P) = 1.8 KW
Time (t) = 2 h per day
Time (t) for 31 days = 2 × 31 = 62 h
Energy (E) =?
E = Pt
E = 1.8 × 62
E = 111.6 KWh
Finally, we shall determine the cost of consumption. This can be obtained as follow:
1 KWh = 15.5 cents
Therefore,
111.6 KWh = 111.6 KWh × 15.5 cents / 1 KWh
111.6 KWh = 1729.8 cents
Converting 1729.8 cents to dollar, we have:
100 cents = $ 1
Therefore,
1729.8 cents = 1729.8 cents × $ 1 / 100 cents
1729.8 cents = $ 17.3
Thus, it will cost $ 17.3 per month to run the electric heater.
Answer:
1.94601 rad/s
Explanation:
= Moment of inertia of carousel = 124 kgm²
= Angular speed of carousel = 3.5 rad/s
= Angular speed of person
r = Radius of carousel = 1.53 m
m = Mass of person = 42.3 kg
Moment of inertia of person
As the angular momentum is conserved in the system
The angular speed of the carousel after the person climbs aboard is 1.94601 rad/s
