Answer:
3.7 km
62.7175453187 seconds
Explanation:
t = Time taken
u = Initial velocity
v = Final velocity
s = Displacement
a = Acceleration
g = Acceleration due to gravity = 9.81 m/s²
![s=ut+\dfrac{1}{2}at^2\\\Rightarrow s=0\times t+\dfrac{1}{2}\times 15\times 10^2\\\Rightarrow s=750\ m](https://tex.z-dn.net/?f=s%3Dut%2B%5Cdfrac%7B1%7D%7B2%7Dat%5E2%5C%5C%5CRightarrow%20s%3D0%5Ctimes%20t%2B%5Cdfrac%7B1%7D%7B2%7D%5Ctimes%2015%5Ctimes%2010%5E2%5C%5C%5CRightarrow%20s%3D750%5C%20m)
![v=u+at\\\Rightarrow v=0+15\times 10\\\Rightarrow v=150\ m/s](https://tex.z-dn.net/?f=v%3Du%2Bat%5C%5C%5CRightarrow%20v%3D0%2B15%5Ctimes%2010%5C%5C%5CRightarrow%20v%3D150%5C%20m%2Fs)
![s=ut+\dfrac{1}{2}at^2\\\Rightarrow s=150\times 5+\dfrac{1}{2}\times 10\times 5^2\\\Rightarrow s=875\ m](https://tex.z-dn.net/?f=s%3Dut%2B%5Cdfrac%7B1%7D%7B2%7Dat%5E2%5C%5C%5CRightarrow%20s%3D150%5Ctimes%205%2B%5Cdfrac%7B1%7D%7B2%7D%5Ctimes%2010%5Ctimes%205%5E2%5C%5C%5CRightarrow%20s%3D875%5C%20m)
![v=u+at\\\Rightarrow v=150+10\times 5\\\Rightarrow v=200\ m/s](https://tex.z-dn.net/?f=v%3Du%2Bat%5C%5C%5CRightarrow%20v%3D150%2B10%5Ctimes%205%5C%5C%5CRightarrow%20v%3D200%5C%20m%2Fs)
![v^2-u^2=2as\\\Rightarrow s=\dfrac{v^2-u^2}{2a}\\\Rightarrow s=\dfrac{0^2-200^2}{2\times -9.81}\\\Rightarrow s=2038.73598369\ m](https://tex.z-dn.net/?f=v%5E2-u%5E2%3D2as%5C%5C%5CRightarrow%20s%3D%5Cdfrac%7Bv%5E2-u%5E2%7D%7B2a%7D%5C%5C%5CRightarrow%20s%3D%5Cdfrac%7B0%5E2-200%5E2%7D%7B2%5Ctimes%20-9.81%7D%5C%5C%5CRightarrow%20s%3D2038.73598369%5C%20m)
The maximum altitude of the rocket is 750+875+2038.73598369 = 3663.73598369 m = 3.7 km
![s=ut+\frac{1}{2}at^2\\\Rightarrow 3663.73598369=0t+\frac{1}{2}\times 9.81\times t^2\\\Rightarrow t=\sqrt{\frac{3663.73598369\times 2}{9.81}}\\\Rightarrow t=27.3301854818\ s](https://tex.z-dn.net/?f=s%3Dut%2B%5Cfrac%7B1%7D%7B2%7Dat%5E2%5C%5C%5CRightarrow%203663.73598369%3D0t%2B%5Cfrac%7B1%7D%7B2%7D%5Ctimes%209.81%5Ctimes%20t%5E2%5C%5C%5CRightarrow%20t%3D%5Csqrt%7B%5Cfrac%7B3663.73598369%5Ctimes%202%7D%7B9.81%7D%7D%5C%5C%5CRightarrow%20t%3D27.3301854818%5C%20s)
Time taken to reach the ground from max height 27.3301854818 seconds
![v=u+at\\\Rightarrow t=\dfrac{v-u}{a}\\\Rightarrow t=\dfrac{0-200}{-9.81}\\\Rightarrow t=20.3873598369\ s](https://tex.z-dn.net/?f=v%3Du%2Bat%5C%5C%5CRightarrow%20t%3D%5Cdfrac%7Bv-u%7D%7Ba%7D%5C%5C%5CRightarrow%20t%3D%5Cdfrac%7B0-200%7D%7B-9.81%7D%5C%5C%5CRightarrow%20t%3D20.3873598369%5C%20s)
Time to reach max height during free fall after stage 2 ends is 20.3873598369 s
Total time of flight is 10+5+20.3873598369+27.3301854818 = 62.7175453187 seconds
Answer:
the constant force applied by Kitty is 8 N.
Explanation:
Given;
work done by Kitty, W = 32 J
distance moved by Kitty's trolley, d = 4 m
Let the constant force applied by Kitty = F
The work done by Kitty is calculated as follows;
W = F x d
F = W / d
F = 32 / 4
F = 8 N.
Therefore, the constant force applied by Kitty is 8 N.
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Answer:
Car C
Explanation:
It is given that,
Five race cars speed toward the finish line at the Jasper County Speedway. The mass of each car has same mass. The speed of all cars are given as :
Car A = 890 m/s
car B = 850 m/s
Car C = 790 m/s
Car D = 895 m/s
Car E = 870 m/s
The distance is constant because the finish line is same for all cars. The speed of an object is given by the total distance covered divided by total time taken i.e.
![s=\dfrac{d}{t}](https://tex.z-dn.net/?f=s%3D%5Cdfrac%7Bd%7D%7Bt%7D)
Where
d = distance
t = time required by the car to come to a full stop
![t=\dfrac{d}{s}](https://tex.z-dn.net/?f=t%3D%5Cdfrac%7Bd%7D%7Bs%7D)
So, time taken is inversely proportional to the speed of the car. The car having less speed will take maximum time to come to stop. Hence, car C will require longest time to come to a full stop.