Answer:
[tex]F=-18412.9N[/tex], where the minus indicates the direction is opposite to that of the throw.
Explanation:
a)
Since MKS stands for meter-kilogram-second and we know that:
[tex]1\ hour = 3600\ seconds[/tex]
[tex]1\ mile = 1600\ meters[/tex]
[tex]1000g = 1kg[/tex]
We can write that:
[tex]\frac{1\ hour}{3600\ seconds}=1[/tex]
[tex]\frac{1600\ meters}{1\ mile}=1[/tex]
[tex]\frac{1kg}{1000g}=1[/tex]
These are conversion factors, equal to 1, so multiplying our results by them won't change their value, only their units.
So we have that:
[tex]90 mph=90 \frac{miles}{hour}(\frac{1\ hour}{3600\ seconds})(\frac{1600\ meters}{1\ mile})=40m/s[/tex]
[tex]110 mph=110 \frac{miles}{hour}(\frac{1\ hour}{3600\ seconds})(\frac{1600\ meters}{1\ mile})=48.89m/s[/tex]
[tex]145 g=145 g(\frac{1kg}{1000g})=0.145kg[/tex]
b)
Newton's 2nd Law tells us that F=ma, and the definition of acceleration is [tex]a=\frac{\Delta v}{\Delta t}[/tex], so we have:
[tex]F=m\frac{\Delta v}{\Delta t}=m\frac{v_f-v_i}{t}[/tex]
Taking the throw direction as the positive one, for our values we have:
[tex]F=m\frac{v_f-v_i}{t}=(0.145kg)\frac{(-48.89m/s)-(+40m/s)}{0.0007s}=-18412.9N[/tex]