part 1 of 3\nlet ( h = s(t) = 50t - 16t^{2} ) give the height of the ball at time ( t ).\nthen the balls…

part 1 of 3\nlet ( h = s(t) = 50t - 16t^{2} ) give the height of the ball at time ( t ).\nthen the balls velocity at time ( t = a ) can be found by\n( v(a)=lim_{t\rightarrow a}\frac{s(t)-s(a)}{t - a} ).\nwe are requested to find the velocity at ( t = 2 ); therefore we use ( a = 2 ) and have\n( v(2)=lim_{t\rightarrow 2}\frac{s(t)-s(2)}{t - 2} )\n( =lim_{t\rightarrow 2}\frac{(50t - 16t^{2})-(50(quad)-16(2)^{2})}{t - 2} )\n( =lim_{t\rightarrow 2}\frac{(50t - 16t^{2})-36}{t - 2} ).

part 1 of 3\nlet ( h = s(t) = 50t - 16t^{2} ) give the height of the ball at time ( t ).\nthen the balls velocity at time ( t = a ) can be found by\n( v(a)=lim_{t\rightarrow a}\frac{s(t)-s(a)}{t - a} ).\nwe are requested to find the velocity at ( t = 2 ); therefore we use ( a = 2 ) and have\n( v(2)=lim_{t\rightarrow 2}\frac{s(t)-s(2)}{t - 2} )\n( =lim_{t\rightarrow 2}\frac{(50t - 16t^{2})-(50(quad)-16(2)^{2})}{t - 2} )\n( =lim_{t\rightarrow 2}\frac{(50t - 16t^{2})-36}{t - 2} ).

Answer

Explanation:

Step1: Substitute (a = 2) into (s(a))

We know (s(t)=50t - 16t^{2}), so (s(2)=50\times2-16\times2^{2}).

Step2: Calculate (s(2))

[ \begin{align*} s(2)&=50\times2-16\times4\ &=100 - 64\ &=36 \end{align*} ]

Answer:

The value to fill in the blank is (2) (from (s(a)) with (a = 2) in the first - level blank).