Answer
$2.49\times 10^5\frac{mi}{h}$
Work Step by Step
We know that
$p_{ball}=m_{ball}v_{ball}$
This can be rearranged as:
$v_{ball}=\frac{p_{ball}}{m_{ball}}$
but given that $p_{ball}=p_{car}$
$\implies v_{ball}=\frac{p_{car}}{m_{ball}}$
We plug in the known values to obtain:
$v_{ball}=\frac{15800}{0.412}=1.11\times 10^6\frac{m}{s}$
Now we convert this speed into miles per hour
$v_{ball}=(\frac{11.6\times 10^6m}{s})(\frac{3600s}{h})(\frac{1mi}{1609m})$
$v_{ball}=2.49\times 10^5\frac{mi}{h}$