Question

Use a(t) = -32 ft/sec^2 as the acceleration due to gravity. (Neglect air resistance.) With what initial velocity must an object be thrown upward (from ground level) to reach the top of a national monument (580 feet)? (Round your answer to three decimal places.) Use a(t) = -32 ft/sec^2 as the acceleration due to gravity. (Neglect air resistance.) A balloon, rising vertically with a velocity of 16 feet per second, releases a sandbag at the instant when the balloon is 32 feet above the ground.

(a) How many seconds after its release will the bag strike the ground? (Round your answer to two decimal places.) sec

(b) At what velocity will it strike the ground? (Round your answer to three decimal places.)

Answer 1

Answer:

Initial velocity    192.666 ft/sec

a) 1.41 sec

Step-by-step explanation:

Equations for

V(f)  = V₀ ± at

V(f)²  =( V₀)² ± 2 a*d

d =   V₀*t  ±  a*t²/2

We are going to use a(t)  =  g  = 32 ft/sec²

a) V₀   =  ??         a = -g      

Then   as  d = 580 ft       and  V(f)  =  0

we have

V(f)²  =  ( V₀)²  - 2*32*580      ⇒  ( V₀)²   = 64*580  (ft²/sec²)

( V₀)²   =  37120          V₀  = 192,666 ft/sec      

a)  t  = ??   in this case V₀ = 0

d  =    V₀*t + gt²/2       ⇒    32  =   ( 32 t²)  /2

t²  = 2  

t =   1.41 sec