Question

A body rises vertically from the earth according to the law s = 64t – 16t2. If it has lost k times its velocity in its 48 ft rise, then k =

Answer 1

v = ds/dt = 64 - 32t

at t = 0 , v = 64
when s = 48
48 = 64t - 16t^2
t^2 - 4t + 3 = 0
(t-1))(t -3) = 0
t = 1 or t = 3
at t = 1, it is still rising
v = 64 - 16 = 48

so 64k = 48
k = 48/64 = 3/4

Answer 2

v = ds/dt = 64 - 32t 

at t = 0 , v = 64 
when s = 48 
48 = 64t - 16t^2 
t^2 - 4t + 3 = 0 
(t-1))(t -3) = 0 
t = 1 or t = 3 
at t = 1, it is still rising 
v = 64 - 32= 32

So 64k=32
K= 1/2