Answer:
68cm
Explanation:
You can solve this problem by using the momentum conservation and energy conservation. By using the conservation of the momentum you get
![p_f=p_i\\mv_1+Mv_2=(m+M)v](https://tex.z-dn.net/?f=p_f%3Dp_i%5C%5Cmv_1%2BMv_2%3D%28m%2BM%29v)
m: mass of the bullet
M: mass of the pendulum
v1: velocity of the bullet = 410m/s
v2: velocity of the pendulum =0m/s
v: velocity of both bullet ad pendulum joint
By replacing you can find v:
![(0.038kg)(410m/s)+0=(0.038kg+4.2kg)v\\\\v=3.67\frac{m}{s}](https://tex.z-dn.net/?f=%280.038kg%29%28410m%2Fs%29%2B0%3D%280.038kg%2B4.2kg%29v%5C%5C%5C%5Cv%3D3.67%5Cfrac%7Bm%7D%7Bs%7D)
this value of v is used as the velocity of the total kinetic energy of the block of pendulum and bullet. This energy equals the potential energy for the maximum height reached by the block:
![E_{fp}=E_{ki}\\\\(m+M)gh=\frac{1}{2}mv^2](https://tex.z-dn.net/?f=E_%7Bfp%7D%3DE_%7Bki%7D%5C%5C%5C%5C%28m%2BM%29gh%3D%5Cfrac%7B1%7D%7B2%7Dmv%5E2)
g: 9.8/s^2
h: height
By doing h the subject of the equation and replacing you obtain:
![(0.038kg+4.2kg)(9.8m/s^2)h=\frac{1}{2}(0.038kg+4.2kg)(3.67m/s)^2\\\\h=0.68m](https://tex.z-dn.net/?f=%280.038kg%2B4.2kg%29%289.8m%2Fs%5E2%29h%3D%5Cfrac%7B1%7D%7B2%7D%280.038kg%2B4.2kg%29%283.67m%2Fs%29%5E2%5C%5C%5C%5Ch%3D0.68m)
hence, the heigth is 68cm
Answer:
6 N
Explanation:
= Mass flow rate = 1 kg/s
v = Final velocity = 6 m/s
u = Initial velocity = 0 m/s
Force is obtained when we divide change in momentum by time
![F=\dfrac{m(v-u)}{t}\\\Rightarrow F=\dfrac{m}{t}(v-u)\\\Rightarrow F=1(6-0)\\\Rightarrow F=6\ N](https://tex.z-dn.net/?f=F%3D%5Cdfrac%7Bm%28v-u%29%7D%7Bt%7D%5C%5C%5CRightarrow%20F%3D%5Cdfrac%7Bm%7D%7Bt%7D%28v-u%29%5C%5C%5CRightarrow%20F%3D1%286-0%29%5C%5C%5CRightarrow%20F%3D6%5C%20N)
The force the person exert on the extinguisher in order to prevent it from accelerating is 6 N
Kinetic of automobile
Mass m = 1,250 Kg; V = 11 m/s
Formula: K.E = 1/2 mV²
K.E = 1/2(1,250 Kg)(11 m/s)²
K.E = 75,625 J
Speed required for insect to have the same kinetic energy as automobile
Mass of insect = 0.72 g convert to Kg m = 7.2 x 10⁻⁴ Kg
K.E = 1/2 mV² Derive V =?
V = 2 K.E/m
V = √2(75,625 J)/7.2 x 10⁻4 Kg
V = √2.1 x 10⁸ m²/s²
V = 14,491.34 m/s (velocity of insect)