Answer:
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Explanation:
Given
<em>Represent mass of April with M and mass of the suitcase with m; such that</em>
<em />![M = 65kg](https://tex.z-dn.net/?f=M%20%3D%2065kg)
![m = 15kg](https://tex.z-dn.net/?f=m%20%3D%2015kg)
<em>Represent initial velocity of April with U and initial velocity of the suitcase with u; such that</em>
(because she's resting on the skateboard, initially)
![u = 3m/s](https://tex.z-dn.net/?f=u%20%3D%203m%2Fs)
<em>After she catches the suitcase, she, the skateboard and the suitcase moves at the same velocity.</em>
Represent this velocity with v
The above given information can be representing using law of conservation of momentum.
![MU + mu = (M + m)v](https://tex.z-dn.net/?f=MU%20%2B%20mu%20%3D%20%28M%20%2B%20m%29v)
Substitute the values of M,U, m and u.
This gives
![65 * 0 + 15 * 3 = (65 + 15)v](https://tex.z-dn.net/?f=65%20%2A%200%20%2B%2015%20%2A%203%20%3D%20%2865%20%2B%2015%29v)
![0 + 45 = (80)v](https://tex.z-dn.net/?f=0%20%2B%2045%20%3D%20%2880%29v)
![45 = 80v](https://tex.z-dn.net/?f=45%20%3D%2080v)
Divide both sides by 80
![\frac{45}{80} = \frac{80v}{80}](https://tex.z-dn.net/?f=%5Cfrac%7B45%7D%7B80%7D%20%3D%20%5Cfrac%7B80v%7D%7B80%7D)
![0.5625 = v](https://tex.z-dn.net/?f=0.5625%20%3D%20v)
<em>Hence, they moved at a velocity of 0.5625m/s</em>