Respuesta :
Answer:
maximum height reached = 35 feet
and [tex]f(t) = 48t-16.07t^{2}[/tex]
Step-by-step explanation:
writing linear motion equations
[tex]s = ut + \frac{1}{2}at^{2}[/tex]
where s is the total displacement, u the initial velocity, t the time travelled, and a is the acceleration.
given u = 48 ft/s, and a = acceleration due to gravity g = -9.8[tex]\frac{m}{s^{2}}[/tex]
1 m = 3.28 feet therefore g becomes -9.8×3.28[tex]\frac{ft}{s^{2}}[/tex]
here negative sigh comes as acceleration due to gravity is in opposite direction of initial velocity.
therefore f(t) becomes [tex]f(t) = 48t-16.07t^{2}[/tex]
to find max height we should find differentiation of f(t) and equate it to 0
therefore we get 48 = 32.144t
t = 1.49 s
therefore max height f(1.49) = 71.67-36.67 = 35 feet
