Answer:
The error he made was that he didn't convert the unit of temperature to Kelvin.
The correct efficiency is 24%
Explanation:
Parameters given:
Temperature of hot reservoir = 100°C = 373 K
Temperature of cold reservoir = 10°C = 273 K
The efficiency of a heat engine is given as:
E = 1 - (Qc/Qh) = 1 - (Tc/Th)
Where
Qc = Output heat;
Qh = Input heat;
Tc = Temperature of the cold reservoir;
Th = Temperature of the hot reservoir.
=> E = 1 - (283/373)
E = 1 - 0.76
E = 0.24
In percentage,
E = 0.24 * 100 = 24%
Hence, the efficiency of the engine is actually 24%.
The error he made was that he didn't convert the temperature to Kelvin. If we leave the temperatures in °C, we have that:
E = 1 - (10/100)
E = 1 - 0.1 = 0.9
In percentage,
E = 0.9 * 100 = 90%
Explanation:
The runner was 8.6km away from the finish line when the bird starts flying.
Therefore it takes the bird 8.6/14.4 = 0.60 hours for the bird to fly to the finish line.
In that 0.60 hours, the runner would have ran an extra 3.6km/h * 0.6h = 2.16km.
Now, the runner and the bird are flying towards each other. The distance between them is 8.6 - 2.16 = 6.44km and their combined speed is 18.0km.
Hence, they will meet in 6.44/18.0 = 0.36 hours.
Overall, the bird flew for 0.60 + 0.36 = 0.96 hours, and flew 14.4km/h * 0.96h = 13.8km.
When the cannonball is shot upwards, kinetic energy converts to gravitational potential energy (GPE).
As the ball rises, speed decreases and height increases.
So when the cannonball has reached its maximum height, all of the Kinetic energy has transferred into gravitational potential energy.
(Because at the max height, the cannonball for a brief moment has no velocity, and thus no kinetic energy)
So the GPE is 48279 Joules at it's maximum height.
