MileenaKitana
13.10.2021 •
Physics
Eric is participating in a pumpkin-launching competition using a homemade air cannon. He collected three points of data from his launch, but wants to determine some specifics about the launch from the data. The table contains the data he collected.
Time from Launch, t (seconds) Height of Pumpkin, h (feet)
0 0
2 272
10.5 0
Use this data to complete the task.
Part A
The motion of a projectile, comparing height over time, can be modeled using a quadratic function. To model this situation with a quadratic function, first identify two of the factors of the quadratic by identifying the zeros in the data points.
Part B
Now that you have two factors, you need to determine what constant to multiply them by to find the actual function. To do this, let c represent the unknown constant, t represent time, and h represent height. Then, use the middle data point to find the value of c and write a function to model the situation. Show your work.
Part C
All projectile motion situations can be modeled by the function , where a represents the vertical acceleration acting on the projectile (this is generally the acceleration due to gravity), represents the initial vertical velocity of the projectile, and represents the initial height of the object.
Using this information, what is the initial vertical velocity of the pumpkin when it is launched?
Part D
The maximum height of the pumpkin will occur exactly halfway between the zeros of the function. Determine the maximum height Eric’s pumpkin will reach during its flight. Show your work.
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Ответ:
The distance from the starting point is (-11.97 Km, 31.78 Km)
Explanation:
The easiest method for this problem is the analytical calculation of the distance traveled by the hiker, we will decompose each vector and find the result in each direction
Va= 15 Km 59º
Vax= 15 cos 59= 7.73 Km
Vay= 15 sin 59= 12.86 Km
Vbx= 23 cos 340= 21.61 Km
Vby= 23 sin 340= -7.87 Km
Vcx= 22 cos 125= -12.62 Km
Vcy= 22 sin 125 = 18.02 Km
Vdx= 30 cos 163= -28.69 Km
Vdy = 30 sin163 = 8.77 Km
We find each component of the total movement
Vtx= Vax+ Vbx+ Vcx+ Vdx
Vty = Vay+ Vby+ Vcy+Vdy
Vtx= 7.73+ 21.61-12.62-28.69
Vtx = -11.97 Km
Vty= Vay+ Vby+ Vcy+ Vdy
Vty= 12.86-7.87+ 18.02+ 8.77
Vty= 31.78 Km
The distance from the starting point is (-11.97 Km, 31.78 Km)
To know what distance to advanced we add the total distances to the value of the initial distance
(41Km,41Km) = (Vox,Voy)
Dx= Vtx +Vox
Dy = Vty + Voy
Dx= -11.97 + 41= 29.03 Km
Dy = 31.78 + 41= 72.78 Km
This is the total distance advanced by the hiker