Answer:
(a) 9.6
(b) [tex]17 - 3.72a[/tex]
(c) 9.1 s
Explanation:
Velocity is the time-derivative of position. From the question,
[tex]H = 17t − 1.86t^2[/tex]
[tex]v(t) = \dfrac{d}{dt}H = 17-3.72t[/tex]
(a) When [tex]t=2[/tex]
[tex]v(t) = 17-3.72\times2 = 17 - 7.44 = 9.56 = 9.6 \text { to 1 decimal place}[/tex]
(b) When [tex]t=a[/tex]
[tex]v(a) = 17-3.72a[/tex]
(c) The rock will hit the surface when When [tex]H=0[/tex].
[tex]H = 17t − 1.86t^2 = 0[/tex]
[tex]t(17 − 1.86t) = 0[/tex]
[tex]t = 0[/tex] (This is when the rock was thrown)
or
[tex]17 − 1.86t = 0[/tex]
[tex]17 = 1.86t[/tex]
[tex]t = \dfrac{17}{1.86} = 9.1398 = 9.1\text { to 1 decimal place}[/tex]
