Answer
$$v=-70$$
Work Step by Step
The object will impact the ground when $s(t)$ becomes zero; that is,$$s(t)=-4.9t^2+250=0 \quad \Rightarrow \quad t=\frac{50}{7}$$.Now, we can find the velocity of the object when it impacts the ground by substituting $a=\frac{50}{7}$ into the definition of velocity given in the question as follows.$$v(a=\frac{50}{7})=\lim_{t \to \frac{50}{7}}\frac{s(\frac{50}{7})-s(t)}{\frac{50}{7}-t}=\lim_{t \to \frac{50}{7}}\frac{(-4.9((\frac{50}{7})^2)+250)-(-4.9t^2+250)}{\frac{50}{7}-t}=\lim_{t \to \frac{50}{7}}\frac{4.9(t^2-(\frac{50}{7})^2)}{\frac{50}{7}-t}=\lim_{x \to \frac{50}{7}} - \frac{4.9(t+\frac{50}{7})(t-\frac{50}{7})}{t-\frac{50}{7}}=\lim_{x \to \frac{50}{7}}-4.9(t+\frac{50}{7})=-70.$$
