Answer: -4.4 m/s
Explanation:
This problem can be solved by the Conservation of Momentum principle, which establishes that the initial momentum
must be equal to the final momentum
:
(1)
Where:
(2)
(3)
is the mass of the child
is the initial velocity of the child
is the mass of the adult
is the initial velocity of the adult (it is sitting still)
is the final velocity of the child
is the final velocity of the adult
Substituting (2) and (3) in (1):
(4)
Isolating
:
(5)
(6)
Finally:
This means the velocity of the child is in the opposite direction
Answer:
6.86 meters
Explanation:
Let the compression of the string be represented by x, and the height of projection of the toy rocket be represented by h.
So that;
x = 9 cm = 0.09 m
In its rest position (i.e before the launch), the spring has a stored potential energy which is given as;
PE =
K
=
x 830 x 
= 415 x 0.0081
= 3.3615
The potential energy in the string = 3.36 Joules
Also,
PE = mgh
where: m is the mass, g is the gravitational force and h the height.
m = 50 g = 0.05 kg, g = 9.8 m
Thus,
PE = 0.05 x 9.8 x h
3.3615 = 0.05 x 9.8 x h
3.3615 = 0.49h
⇒ h = 
= 6.8602
The height of the toy rocket would be 6.86 meters.
Answer:
<em>Heat of the reservoir is 461.38 K or 188.1 °C</em>
<em>The heating load is 18.705 kW</em>
Explanation:
COP = 8.7
working temperature
= 248 °C = 248 + 273.3 = 521.3 K
work power W = 2.15 kW
reservoir temperature
= ?
heating load Q = ?
We know that
COP = Q/W
Q = COP x W = 8.7 x 2.15 = <em>18.705 kW</em>
Also,
COP =
= 
8.7 = 
4535.31 - 8.7
= 521.3
4535.31 - 521.3 = 8.7
4014.01 = 8.7
= 4014.01/8.7 = <em>461.38 K</em>
or 461.38 -273.3 = <em>188.1 °C</em>