What Was the Rocket's Initial Velocity?

[Demise]

Here is the problem:

Homer Hickim and his friends shoot off a rocket. A fire is reported 3 miles away from the launch pad (1mile = 5289 feet). Homer and his friends are accused of the fire.

Homer knows that the rocket took 14 seconds to come down from its highest point. This means that the rocket was in the air for about 28 seconds before it hit the ground. Use the following equation from the movie to find out the initial velocity of the rocket in feet per second.

s = 1/2at^2 + vt

a= -32
t= time in seconds
s= altitude in feet
v= initial velocity

14x5280 = 1/2(-32)(28)^2+v(28) <--- this is what i came up with for my equation... I am not sure wether the value of S is right, s=alititude how would i find altitude for this problem?

 

[Doc Al]

Didn't you already have a thread going with this same problem? https://www.physicsforums.com/showthread.php?t=62879

In any case, find the horizontal and vertical components of the initial velocity separately:

Horizontal velocity is constant; use: speed = (horizontal distance)/time.

Vertical direction is accelerated motion: use: v_f = v_i + at (Hint: what's the speed at the top of the motion?) To me, that's the easiest way to find the vertical component of the initial velocity, but you could certainly use the equation "s = 1/2at^2 + vt": just realize that when t = 28 seconds, s = 0 (it comes back down to earth).

Once you find the horizontal and vertical components of the initial velocity, find the total velocity using the Pythagorean theorem.

 

[wais]

To solve Homer's altitude problem, we can use the following equation:

s = 1/2at^2 + vt

Where:
a = acceleration due to gravity, which is -32 ft/s^2
t = time in seconds, which is 28 seconds
s = altitude in feet, which we need to find
v = initial velocity in feet per second, which is what we are looking for

We can plug in the given values and solve for v:

s = 1/2(-32)(28)^2 + v(28)
s = -1568 + 28v

Now, we know that the fire was reported 3 miles away from the launch pad, which is equivalent to 15867 feet. This means that the altitude of the rocket was 15867 feet when it hit the ground. So, we can set s = 15867 and solve for v:

15867 = -1568 + 28v
28v = 17435
v = 622.68 ft/s

Therefore, the initial velocity of the rocket was approximately 622.68 feet per second. This information can be used to determine if Homer and his friends are responsible for the fire, as they can calculate the trajectory of the rocket and see if it matches with the location of the fire.