If the velocity of a body changes from 13 m/s to 30 m/s while undergoing constant acceleration, what's the average velocity of t
2 answers:
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Answer : The temperature of the hot reservoir (in Kelvins) is 1128.18 K
Explanation :
Efficiency of carnot heat engine : It is the ratio of work done by the system to the system to the amount of heat transferred to the system at the higher temperature.
Formula used for efficiency of the heat engine.
where,
= efficiency = 0.780
= Temperature of hot reservoir = ?
= Temperature of cold reservoir =
Now put all the given values in the above expression, we get:
Therefore, the temperature of the hot reservoir (in Kelvins) is 1128.18 K
Answer:
The circus performer falls back down to the ground
Explanation:
The question parameters are;
The initial velocity of the circus performer = 21 m/s
The angle in which the performer launches himself = 75° towards the platform
The height of the platform above the ground = 20 m
The horizontal distance of the platform from the springboard = 15 m
The vertical motion of the circus performer is given by the following projectile motion relation;
y = y₀ + v₀·sinθ₀t-1/2·g·t²
Where;
y = Height reached by the circus performer
y₀ = Initial height of the the circus performer (the springboard) = 0 m
v₀ = Initial velocity of the the circus performer = 21 m/s
θ₀ = The angle with which the circus performer launches himself = 75°
t = The time of ,light of the circus performer
g = The acceleration due to gravity
Therefore, when the height is 20 m, we have;
20 = 21*sin(75)*t - 1/2*9.81*t²
Which gives;
21*sin(75)*t - 1/2*9.81*t² - 20 = 0
Factorizing using a graphing calculator, gives;
t = 1.623 or t = 2.513
Therefore, the circus performer passes the 20 m mark twice, in his motion, where the first time is when he is on his way up while the second time is when he is on his way down
The horizontal motion of the circus performer is given by the following projectile motion relation;
x = x₀ + v₀*cos(θ₀)* t
Where;
x₀ = The initial position of the circus performer in relation to the final position = 0
Plugging in the value of t when y = 20, we get;
x = 21×cos(75)×1.623 = 8.82 m, which is less than the 15 m platform distance from the spring board
Checking the other time value, we have;
x = 21×cos(75)×2.513 = 13.66 m which is also less than the 15 m platform distance from the spring board
Therefore, the circus performer misses the platform and falls back down to the ground.
