(a) 933.33W
(b) 3.36 x 10⁶J
<h2>Explanation:</h2>(a) Power is the time rate of change of energy.
In the question, the runner expends 800 kilocalories (kcal) of energy in one hour (h).
That means that power expended is 800 kcal / h.
To get the power in Watts, we convert 800 kcal/h to Joules per second (J/s) as follows;
(i) First convert kcal to Joules (J)
1 cal = 4.2 J
1 kcal = 1 x 1000 cal = 1 x 1000 cal x 4.2 J / 1 cal = 4200 J
(ii) Then convert 1 hour to second (s)
1 h = 3600s
(iii) Now convert 800 kcal/h to J/s
800 kcal / h = =
= 933.33J/s = 933.33W
Therefore, the power expended in J/s (or in Watts) is 933.33
(b) According to the question, the runner can run 15km in 1 hour and will expend a power of 933.33W. To calculate the energy expended at this time, we use the formula;
E = P x t -------------------(ii)
Where;
E = Energy
P = Power = 933.33W
t = time taken = 1 hour = 36000s
Substitute these values into equation (ii) as follows;
E = 933.33 x 3600
E = 3359988 J
E = 3.36 x 10⁶ J
Therefore, the total energy is 3.36 x 10⁶J
Answer:
(a) The range of the projectile is 31,813.18 m
(b) The maximum height of the projectile is 4,591.84 m
(c) The speed with which the projectile hits the ground is 670.82 m/s.
Explanation:
Given;
initial speed of the projectile, u = 600 m/s
angle of projection, θ = 30⁰
acceleration due to gravity, g = 9.8 m/s²
(a) The range of the projectile in meters;
(b) The maximum height of the projectile in meters;
(c) The speed with which the projectile hits the ground is;
Answer:
The mass of the banana is m and it is at height h.
Applying the Law of Conservation of Energy
Total Energy before fall = Total Energy after fall
=
Here, total energy is the sum of kinetic energy and potential energy
+
=
+
(a)
When banana is at height h, it has
= 0 and
= mgh
and when it reaches the river, it has
= 1/2m
and
= 0
Putting the values in equation (a)
0 + mgh = 1/2m + 0
mgh = 1/2m
<em>cutting 'm' from both sides</em>
<em> </em>gh = 1/2
v =
Hence, the velocity of banana before hitting the water is
v =
Answer:
<em>Answer: Work equals force times distance. 3,000 J</em>
Explanation:
Work Done By A Force
When some force is applied and a displacement
is achieved, the work done by the force is given by
Note that the work is a scalar magnitude as the result of the dot-product of two vectors. If the force and the displacement are parallel, then the vectors can be replaced as its magnitudes F,x and the work is
The dot product becomes a simple arithmetic product, i.e force times distance.
Sara weighs 500 Nw and she climbs up a 6 meter set of stairs. She needs to lift her weight up, so the force is the weight and the distance is the height of the stairs, thus
Answer: Work equals force times distance. 3,000 J