Question

If a ball is thrown vertically upward with a velocity of 160 ft/s, then its height after t seconds is s = 160t − 16t^2.

Answer 1

Answer:

400ft.    32ft/s       -32ft/s

Explanation:

In reality the gravitational acceleration is 9.81 so the quadratic coefficient of the function should be 9.81/2

Anyway for the sake of assumtion let us takes=160t-16t^2

 

ds/dt=160-32t=0

 

t=160/32= 5 seconds.

s=160*160/32-16*(160/32)^2= 400 mts

 

 

s=384 mts

160t-16t^2=384

i.e

16t^2-160t+384=0

 

t^2-10t+24=0

(t-6)(t-4)=0

t=[4,6]

we have to take t=4 because it is all the up i.e <5

 

velocity =v=ds/dt=160-32t

 

v=160-32*4=32 ft/sec still going up

 

for all the way down take t=6 whuch is >5

 

v=160-6*32=-32 ft/sec (falling down!!!)