COMPLETE QUESTION:
Phileas is going on a hot air balloon ride. His height above the ground
after t minutes is a quadratic function of t.
He begins from a platform at a height of 76 meters.
The balloon reaches its maximum height after 30 minutes.
After 80 minutes, he finally lands (at a height of 0 meters)
(a) Give a function f(t) for Phileas’s height above the ground after t minutes.
Answer:
f(t) = (-76/160)t² + (9560/1600)t + 76
Explanation:
Clearly explained in the attachment below
The concept of momentum tells us that it is equivalent to the product between the mass and the velocity of the object, that is to say that in general it can be written as
![p = mv](https://tex.z-dn.net/?f=p%20%3D%20mv)
Where,
m = mass
v = Velocity
Our values are given as,
![m = 0.145kg](https://tex.z-dn.net/?f=m%20%3D%200.145kg)
![v = 67mi/h = 30m/s](https://tex.z-dn.net/?f=v%20%3D%2067mi%2Fh%20%3D%2030m%2Fs)
Replacing we have that,
![p = (0.145)(30)](https://tex.z-dn.net/?f=p%20%3D%20%280.145%29%2830%29)
![p = 12.45 kg\cdot m/s](https://tex.z-dn.net/?f=p%20%3D%2012.45%20kg%5Ccdot%20m%2Fs)
Therefore the magniude of the momentum of the pitched baseball is ![12.45 kg\cdot m/s](https://tex.z-dn.net/?f=12.45%20kg%5Ccdot%20m%2Fs)
Hypothesis: The water will squirt far.
Indep.V.: Height of hole.
Depend.V.: Range of squirt
Constant: Everything that isnt the independant var. such as filled liquid.
Control: None,I believe.
Number of groups: 4
Trials per group: 4
The solution for this problem is through this formula:Ø = w1 t + 1/2 ã t^2
where:Ø - angular displacement w1 - initial angular velocity t - time ã - angular acceleration
128 = w1 x 4 + ½ x 4.5 x 5^2 128 = 4w1 + 56.254w1 = -128 + 56.25 4w1 = 71.75w1 = 71.75/4
w1 = 17.94 or 18 rad s^-1
w1 = wo + ãt
w1 - final angular velocity
wo - initial angular velocity
18 = 0 + 4.5t t = 4 s