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 =
A)1 B) 1/2 C) 1/3 D)1/9

Answer 1

At height 48, we have

64t-16t^2 = 48
t=1 or 3
Since the body is rising (not falling), t=1

v(1) = 64-32*1 = 32
32 = 1/2 * 64
so, k = 1/2

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