e.Digital Corporation (fka EDIG)

[D.inkie]

The SOLUTION : (Assume the Blimp did not ignite on takeoff because of excessive use of green wood.)

1. a = -32
Integrate to obtain v = -32t + c. We will assume the initial velocity is zero so
v = -32t
Integrate to find distance , d = -16t^2 + c. If d represents the distance from the ground, when t = 0, c = 100 so the distance equation is:
d = -16t^2 + 100
When the Blimp lands, d = 0 so solve the equation:
0 = -16t^2 + 100.
This results in t = 2.5 seconds.
So it took 2.5 seconds for the Blimp to land.
Since v(2.5) = -80 ft/sec , the Blimp's velocity at impact was -80 ft/sec.

2. You now need to find a different initial velocity.
Let k = initial velocity.
a = -32
v = -32t +k
So distance = -16t^2 + kt + c. Since when t = 0, c = 100 , the distance equation is:
d = -16t^2 + kt + 100

Since you want the impact (d = 0) to occur at t = 1.25 seconds, solve the equation:
0 = -16(1.25)^2 + 1.25k + 100

This results in k = -60 ft/sec.
Thus, the initial velocity is -60 ft/sec
So the new velocity equation is :
v = -32t - 60
So v(1.25) = -100 ft/sec.
So the velocity at impact is - 100 ft/sec.

3. Now let j be the new initial velocity.
v = -32t + j
Since we want the velocity at impact to be -90, solve the velocity equation for t:
-90 = -32t + j Solving for t yields the equation:



The distance equation is:
d = -16t^2 +jt + 100
Substituting the time of impact from the velocity equation results in:



Solving for j yields j = 41.231ft/sec and j = -41.231 ft.sec.
The positive initial velocity would cause the bale to be in flight for 4.101 seconds, much too long for Dad.
The negative initial velocity would only require 1.524 seconds of flight, much more to his liking.
So the desired initial velocity is -41.231 ft/sec.