Answer:
The initial velocity is 314.88 ft/s
The maximum height reached is 144 meter.
Step-by-step explanation:
The total time period is 6 seconds for the raindrop.
Using the equation of motion by differentiating h(t) to give v(t),
[tex]v(t) = -32(t) + 96[/tex]
at t=0, v(0) = 96 m/sec = 314.88 ft/sec
It is given that,
[tex]h(t) = (-16)(t^{2}) + 96t[/tex]
differentiating we get
[tex]v(t) = -32(t) + 96[/tex]
at highest point, v=0;
thus gives us highest point achieved at t=3 seconds.
Height at t=3 seconds is,
[tex]h(t) = (-16)(t^{2}) + 96t = (-16)(3^{2}) + 96(3) = 144 m[/tex]
