Answer:280.216j/kg°C
Explanation:
Mass of metal=0.0663kg
mass of water=0.395kg
Final temperature=27.4°C
Temperature of metal=241°C
Temperature of water=25°C
specific heat capacity of water=4186j/kg°C
0.0663xax(241-27.4)=0.395x4186x(27.4-25)
0.0663xax213.6=0.395x4186x2.4
14.16168a=3968.328
a=3968.328 ➗ 14.16168
a=280.216j/kg°C
The initial velocity is
v(0) = 16.5 ft/s
While in the water, the acceleration is
a(t) = 10 - 0.
![\frac{dv}{dt} =10-0.8v \\\\ \frac{dv}{10-0.8v}=dt \\\\ \int_{16.5}^{v} \, \frac{dv}{10-0.8v} = \int_{0}^{t} dt \\\\ - \frac{1}{0.8} [ln(10-0.8v)]_{16.5}^{v}=t \\\\ ln \frac{10-0.8v}{-3.2}=-0.8t \\\\ \frac{0.8v -10}{3.2} =e^{-0.8t} \\\\ 0.8v = 10 + 3.2e^{-0.8t} \\\\ v=12.5+4e^{-0.08t}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bdv%7D%7Bdt%7D%20%3D10-0.8v%20%5C%5C%5C%5C%20%20%5Cfrac%7Bdv%7D%7B10-0.8v%7D%3Ddt%20%5C%5C%5C%5C%20%5Cint_%7B16.5%7D%5E%7Bv%7D%20%5C%2C%20%20%5Cfrac%7Bdv%7D%7B10-0.8v%7D%20%20%3D%20%5Cint_%7B0%7D%5E%7Bt%7D%20dt%20%5C%5C%5C%5C%20-%20%5Cfrac%7B1%7D%7B0.8%7D%20%5Bln%2810-0.8v%29%5D_%7B16.5%7D%5E%7Bv%7D%3Dt%20%5C%5C%5C%5C%20ln%20%5Cfrac%7B10-0.8v%7D%7B-3.2%7D%3D-0.8t%20%5C%5C%5C%5C%20%20%5Cfrac%7B0.8v%20-10%7D%7B3.2%7D%20%20%3De%5E%7B-0.8t%7D%20%5C%5C%5C%5C%200.8v%20%3D%2010%20%2B%203.2e%5E%7B-0.8t%7D%20%5C%5C%5C%5C%20v%3D12.5%2B4e%5E%7B-0.08t%7D)
The velocity function is

It satisfies the condition that v(0) = 16.5 ft/s.
When t = 5.7s, obtain

The depth of the lake is
![d=\int_{0}^{5.7} \, (12.5+4e^{-0.8t})dt \\\\ = 12.5(5.7)+ \frac{4}{(-0.8)}[e^{-0.8t}]_{0}^{5.7} \\\\ =71.25-5(0.0105-1) =76.198 \, ft](https://tex.z-dn.net/?f=d%3D%5Cint_%7B0%7D%5E%7B5.7%7D%20%5C%2C%20%2812.5%2B4e%5E%7B-0.8t%7D%29dt%20%5C%5C%5C%5C%20%3D%2012.5%285.7%29%2B%20%5Cfrac%7B4%7D%7B%28-0.8%29%7D%5Be%5E%7B-0.8t%7D%5D_%7B0%7D%5E%7B5.7%7D%20%5C%5C%5C%5C%20%3D71.25-5%280.0105-1%29%20%3D76.198%20%5C%2C%20ft)
Answer:
The velocity at the bottom of the lake is 12.5 ft/s
The depth of the lake is 76.2 ft
The maximum force that the athlete exerts on the bag is NEGATIVE 1,500 N and in the OPPOSITE DIRECTION of the force that the bag exerts on the athlete.
<h3>Newton's third law of motion</h3>
Newton's third law of motion states action and reaction are equal and opposite. That is the force applied to an object is equal in magnitude to force experienced by the object but in opposite direction.
From the given question, when the bag exert a certain on the athlete, the athlete also exerts similar force to the bag but in opposite direction.
Thus, the complete sentence is as follows;
The maximum force that the athlete exerts on the bag is NEGATIVE 1,500 N and in the OPPOSITE DIRECTION of the force that the bag exerts on the athlete.
Learn more about Newton's third law of motion here: brainly.com/question/25998091
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Answer: Rr = 900w
T = 1.66×10^-5s
P = 36.92W
Explanation: please find the attached file for the solution.
Answer:
0.95 seconds
Explanation:
t = Time taken
u = Initial velocity = 15 m/s
v = Final velocity
s = Displacement
a = Acceleration = 9.81 m/s² (downward positive, upward negative)
Time taken by the ball to reach the maximum height

Maximum height

Distance between maximum height of the ball and the branch is 11.47-7 = 4.46 m
So, the distance that will be covered on the way down is 4.46 m
Now
u = 0
s = 4.46

Time taken by the ball from the maximum height to the tree branch is 0.95 seconds.
Total time taken from the moment the ball is thrown to reach the tree branch is 1.52+0.95 = 2.47 seconds