The problem is as follows:
A ball of $1\,kg$ in mass is thrown with a speed of $-10\vec{j}\,\frac{m}{s}$ from a height of $15\,m$ to a horizontal floor. Find the modulus of the average force in $N$ that the ball receives from the floor during the impact with the ground which lasts $0.1\,s$ and dissipates $150\,J$. (You may use the value of gravity $g=10\,\frac{m}{s^2}$.
The alternatives given in my book are as follows:
$\begin{array}{ll} 1.&290\,N\\ 2.&300\,N\\ 3.&310\,N\\ 4.&320\,N\\ 5.&330\,N\\ \end{array}$
This problem has left me go in circles as I don't know exactly how should I treat or use the information to obtain the average force?. I'm assuming that there is a conservation of momentum but as I mentioned I don't know what to do?. Can somebody help me here?.
Supposedly the answer is $310\,N$. But the only thing that comes to my mind to find the average force is:
$\overline{\vec{F}}=m\frac{\Delta v}{\Delta t}$
Since there will be a conservation of mechanical energy at the impact it can be found using this analysis. But again I'm not sure how to get to the answer of $310\,N$. Can somebody help me here?.
Velocity before impact = $-20j$ m/s
Energy before impact = $0.5*(1)(20)^2 = 200$ J
Energy after impact = $50$ J
Velocity after impact = $10j $ m/s
Average Net Force = $\frac{10(1)- (-20)(1) }{0.1} = 300j $ N
Average Force of floor = Average Net force - Average Body Force
Hence average force of floor = $300 - (-10) = 310 N$