Answer: The speed is 15.5 m/s
Explanation:
The kinetic energy can be written as:
K = (1/2)*m*v^2
where m is the mass and v is the speed.
Then we have that:
18 j = (1/2)*0.15kg*v^2
Now we solve this for v.
√(18*2/0.15) = v
15.5 m/s = v
The rock will sink.
The density of water is 1.0g/cm^3
The density of the rock is 1.73g/cm^3
#1
mass of Sam = 75 kg
velocity of Sam = 18 m/s
now for momentum we can use
![P = mv](https://tex.z-dn.net/?f=P%20%3D%20mv)
![P = 75(18)](https://tex.z-dn.net/?f=P%20%3D%2075%2818%29%20)
![P = 1350 kg m/s](https://tex.z-dn.net/?f=P%20%3D%201350%20kg%20m%2Fs)
#2
Momentum of football = momentum of bullet
![P_{ball} = P_{bullet}](https://tex.z-dn.net/?f=P_%7Bball%7D%20%3D%20P_%7Bbullet%7D)
![m_{ball}v_{ball} = m_{bullet}v_{bullet}](https://tex.z-dn.net/?f=m_%7Bball%7Dv_%7Bball%7D%20%3D%20m_%7Bbullet%7Dv_%7Bbullet%7D)
![0.25 v = 0.05 (500)](https://tex.z-dn.net/?f=0.25%20v%20%3D%200.05%20%28500%29)
![v = 100 m/s](https://tex.z-dn.net/?f=v%20%3D%20100%20m%2Fs)
#3
As per Newton's law we know that net force is given as
![F = \frac{\Delta P}{\Delta t}](https://tex.z-dn.net/?f=F%20%3D%20%5Cfrac%7B%5CDelta%20P%7D%7B%5CDelta%20t%7D)
now we have
![\Delta P = m(v_f - v_i)](https://tex.z-dn.net/?f=%5CDelta%20P%20%3D%20m%28v_f%20-%20v_i%29)
![\Delta P = 55(20 - 0) = 1100 kg m/s](https://tex.z-dn.net/?f=%5CDelta%20P%20%3D%2055%2820%20-%200%29%20%3D%201100%20kg%20m%2Fs)
also we know that
![\Delta t = 0.5 s](https://tex.z-dn.net/?f=%5CDelta%20t%20%3D%200.5%20s)
form above equation we have
![F = \frac{1100}{0.5} = 2200 N](https://tex.z-dn.net/?f=F%20%3D%20%5Cfrac%7B1100%7D%7B0.5%7D%20%3D%202200%20N)
#4
As per Newton's law we know that net force is given as
![F = \frac{\Delta P}{\Delta t}](https://tex.z-dn.net/?f=F%20%3D%20%5Cfrac%7B%5CDelta%20P%7D%7B%5CDelta%20t%7D)
now we have
![\Delta P = m(v_f - v_i)](https://tex.z-dn.net/?f=%5CDelta%20P%20%3D%20m%28v_f%20-%20v_i%29)
![\Delta P = 0.16(44 - (-38)) = 13.12 kg m/s](https://tex.z-dn.net/?f=%5CDelta%20P%20%3D%200.16%2844%20-%20%28-38%29%29%20%3D%2013.12%20kg%20m%2Fs)
also we know that
![\Delta t = 0.002 s](https://tex.z-dn.net/?f=%5CDelta%20t%20%3D%200.002%20s)
form above equation we have
![F = \frac{13.12}{0.002} = 6560 N](https://tex.z-dn.net/?f=F%20%3D%20%5Cfrac%7B13.12%7D%7B0.002%7D%20%3D%206560%20N)
Answer:
S = Vo t * 1/2 a t^2 equation for distance traveled
w = w0 t + 1/2 a t^2 equivalent circular equation where w equals omega
w = 5.98 * 27.5 + a (27.5)^2/ 2
a = (w2 - w1) / t = -5.98 / 27.5 = -.217
w = 5.98 * 27.5 - 1/2 * .217 * 27.5^2 = 82.4
Since 1 Rev = 2 pi radians
Rev = 82.4 / 2 * pi = 13.1 Rev