The particles themselves do not change in size. When changing state the distance between the particles is what changes due to overcoming the intermolecular forces between the particles.
Answer with Explanation:
We are given that
Mass of one cart,![m_1=2.8 kg](https://tex.z-dn.net/?f=m_1%3D2.8%20kg)
Mass of second cart,![m_2=1.2 kg](https://tex.z-dn.net/?f=m_2%3D1.2%20kg)
Initial velocity of one cart,![u_1=4.6m/s](https://tex.z-dn.net/?f=u_1%3D4.6m%2Fs)
Initial velocity of second cart,![u_2=-2.7 m/s](https://tex.z-dn.net/?f=u_2%3D-2.7%20m%2Fs)
a.Total momentum,![P=m_1u_1+m_2u_2=2.8(4.6)+1.2(-2.7)](https://tex.z-dn.net/?f=P%3Dm_1u_1%2Bm_2u_2%3D2.8%284.6%29%2B1.2%28-2.7%29)
![P=9.64 kgm/s](https://tex.z-dn.net/?f=P%3D9.64%20kgm%2Fs)
b.Velocity of second cart,
=0
According to law of conservation of momentum
Initial momentum=Final momentum
![9.64=2.8v_1+1.2\times 0](https://tex.z-dn.net/?f=9.64%3D2.8v_1%2B1.2%5Ctimes%200)
![v_1=\frac{9.64}{2.8}](https://tex.z-dn.net/?f=v_1%3D%5Cfrac%7B9.64%7D%7B2.8%7D)
![v_1=3.44m/s](https://tex.z-dn.net/?f=v_1%3D3.44m%2Fs)
The bowling ball has more momentum because it has more mass than the golf ball.
Please correct me if I'm wrong!! I'd be happy to fix it!! :)
Before the engines fail
, the rocket's horizontal and vertical position in the air are
![x=\left(103\,\frac{\rm m}{\rm s}\right)\cos53.0^\circ\,t+\dfrac12\left(32.0\,\frac{\rm m}{\mathrm s^2}\right)\cos53.0^\circ t^2](https://tex.z-dn.net/?f=x%3D%5Cleft%28103%5C%2C%5Cfrac%7B%5Crm%20m%7D%7B%5Crm%20s%7D%5Cright%29%5Ccos53.0%5E%5Ccirc%5C%2Ct%2B%5Cdfrac12%5Cleft%2832.0%5C%2C%5Cfrac%7B%5Crm%20m%7D%7B%5Cmathrm%20s%5E2%7D%5Cright%29%5Ccos53.0%5E%5Ccirc%20t%5E2)
![y=\left(103\,\frac{\rm m}{\rm s}\right)\sin53.0^\circ\,t+\dfrac12\left(32.0\,\frac{\rm m}{\mathrm s^2}\right)\sin53.0^\circ t^2](https://tex.z-dn.net/?f=y%3D%5Cleft%28103%5C%2C%5Cfrac%7B%5Crm%20m%7D%7B%5Crm%20s%7D%5Cright%29%5Csin53.0%5E%5Ccirc%5C%2Ct%2B%5Cdfrac12%5Cleft%2832.0%5C%2C%5Cfrac%7B%5Crm%20m%7D%7B%5Cmathrm%20s%5E2%7D%5Cright%29%5Csin53.0%5E%5Ccirc%20t%5E2)
and its velocity vector has components
![v_x=\left(103\,\frac{\rm m}{\rm s}\right)\cos53.0^\circ+\left(32.0\,\frac{\rm m}{\mathrm s^2}\right)\cos53.0^\circ t](https://tex.z-dn.net/?f=v_x%3D%5Cleft%28103%5C%2C%5Cfrac%7B%5Crm%20m%7D%7B%5Crm%20s%7D%5Cright%29%5Ccos53.0%5E%5Ccirc%2B%5Cleft%2832.0%5C%2C%5Cfrac%7B%5Crm%20m%7D%7B%5Cmathrm%20s%5E2%7D%5Cright%29%5Ccos53.0%5E%5Ccirc%20t)
![v_y=\left(103\,\frac{\rm m}{\rm s}\right)\sin53.0^\circ+\left(32.0\,\frac{\rm m}{\mathrm s^2}\right)\sin53.0^\circ t](https://tex.z-dn.net/?f=v_y%3D%5Cleft%28103%5C%2C%5Cfrac%7B%5Crm%20m%7D%7B%5Crm%20s%7D%5Cright%29%5Csin53.0%5E%5Ccirc%2B%5Cleft%2832.0%5C%2C%5Cfrac%7B%5Crm%20m%7D%7B%5Cmathrm%20s%5E2%7D%5Cright%29%5Csin53.0%5E%5Ccirc%20t)
After
, its position is
![x=273\,\rm m](https://tex.z-dn.net/?f=x%3D273%5C%2C%5Crm%20m)
![y=362\,\rm m](https://tex.z-dn.net/?f=y%3D362%5C%2C%5Crm%20m)
and the rocket's velocity vector has horizontal and vertical components
![v_x=120\,\frac{\rm m}{\rm s}](https://tex.z-dn.net/?f=v_x%3D120%5C%2C%5Cfrac%7B%5Crm%20m%7D%7B%5Crm%20s%7D)
![v_y=159\,\frac{\rm m}{\rm s}](https://tex.z-dn.net/?f=v_y%3D159%5C%2C%5Cfrac%7B%5Crm%20m%7D%7B%5Crm%20s%7D)
After the engine failure
, the rocket is in freefall and its position is given by
![x=273\,\mathrm m+\left(120\,\frac{\rm m}{\rm s}\right)t](https://tex.z-dn.net/?f=x%3D273%5C%2C%5Cmathrm%20m%2B%5Cleft%28120%5C%2C%5Cfrac%7B%5Crm%20m%7D%7B%5Crm%20s%7D%5Cright%29t)
![y=362\,\mathrm m+\left(159\,\frac{\rm m}{\rm s}\right)t-\dfrac g2t^2](https://tex.z-dn.net/?f=y%3D362%5C%2C%5Cmathrm%20m%2B%5Cleft%28159%5C%2C%5Cfrac%7B%5Crm%20m%7D%7B%5Crm%20s%7D%5Cright%29t-%5Cdfrac%20g2t%5E2)
and its velocity vector's components are
![v_x=120\,\frac{\rm m}{\rm s}](https://tex.z-dn.net/?f=v_x%3D120%5C%2C%5Cfrac%7B%5Crm%20m%7D%7B%5Crm%20s%7D)
![v_y=159\,\frac{\rm m}{\rm s}-gt](https://tex.z-dn.net/?f=v_y%3D159%5C%2C%5Cfrac%7B%5Crm%20m%7D%7B%5Crm%20s%7D-gt)
where we take
.
a. The maximum altitude occurs at the point during which
:
![159\,\frac{\rm m}{\rm s}-gt=0\implies t=16.2\,\rm s](https://tex.z-dn.net/?f=159%5C%2C%5Cfrac%7B%5Crm%20m%7D%7B%5Crm%20s%7D-gt%3D0%5Cimplies%20t%3D16.2%5C%2C%5Crm%20s)
At this point, the rocket has an altitude of
![362\,\mathrm m+\left(159\,\frac{\rm m}{\rm s}\right)(16.2\,\rm s)-\dfrac g2(16.2\,\rm s)^2=1650\,\rm m](https://tex.z-dn.net/?f=362%5C%2C%5Cmathrm%20m%2B%5Cleft%28159%5C%2C%5Cfrac%7B%5Crm%20m%7D%7B%5Crm%20s%7D%5Cright%29%2816.2%5C%2C%5Crm%20s%29-%5Cdfrac%20g2%2816.2%5C%2C%5Crm%20s%29%5E2%3D1650%5C%2C%5Crm%20m)
b. The rocket will eventually fall to the ground at some point after its engines fail. We solve
for
, then add 3 seconds to this time:
![362\,\mathrm m+\left(159\,\frac{\rm m}{\rm s}\right)t-\dfrac g2t^2=0\implies t=34.6\,\rm s](https://tex.z-dn.net/?f=362%5C%2C%5Cmathrm%20m%2B%5Cleft%28159%5C%2C%5Cfrac%7B%5Crm%20m%7D%7B%5Crm%20s%7D%5Cright%29t-%5Cdfrac%20g2t%5E2%3D0%5Cimplies%20t%3D34.6%5C%2C%5Crm%20s)
So the rocket stays in the air for a total of
.
c. After the engine failure, the rocket traveled for about 34.6 seconds, so we evalute
for this time
:
![273\,\mathrm m+\left(120\,\frac{\rm m}{\rm s}\right)(34.6\,\rm s)=4410\,\rm m](https://tex.z-dn.net/?f=273%5C%2C%5Cmathrm%20m%2B%5Cleft%28120%5C%2C%5Cfrac%7B%5Crm%20m%7D%7B%5Crm%20s%7D%5Cright%29%2834.6%5C%2C%5Crm%20s%29%3D4410%5C%2C%5Crm%20m)