Translational motion

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TBR Physics chapter 1

Cos (0 degrees) in fraction

√4 / 2 = 2 / 2

cos (0 degrees) in decimal

1.00

Cos (30 degrees) in fraction

√3 / 2 = 1.73 / 2

cos (30 degrees) in decimal

0.86

cos (45 degrees) in fraction

√2 / 2 = 1.41 / 2

cos (45 degrees) in decimal

0.71

cos (60 degrees) in fraction

√1 / 2 = 1 / 2

cos (60 degrees) in decimal

0.50

cos (90 degrees) in fraction

0 / 2

cos (90 degrees) in decimal

0

sin (0 degrees) in fraction

0 / 2

sin (0 degrees) in decimal

0

sin (30 degrees) in fraction

√1 / 2 = 1 / 2

sin (30 degrees) in decimal

0.5

sin (45 degrees) in fraction

√2 / 2 = 1.41 / 2

sin (45 degrees) in decimal

0.71

sin (60 degrees) in fraction

√3 / 2= 1.73 / 2

sin (60 degrees) in decimal

0.86

sin (90 degrees) in fraction

√4 / 2 = 2 / 2

sin (90 degrees) in decimal

1.00

tan (0 degrees)

0 / 1 = 0

tan (30 degrees)

0.50 / 0.86 = 0.58

tan (45 degrees)

0.71 / 0.71 = 1

tan (60 degrees)

0.86/ 0.50 = 1.73

tan (90 degrees)

1 / 0 = undefined

How do you go from A² = Ax² + Ay²
to 1 = cos²θ + sin²θ?

Ax = Acosθ
Ay = Asinθ
A² = A² Cos²θ + A²sin²θ
A² = A²(cos²θ + sin²θ )

Which equation of uniformly accelerated motion is missing the "v" variable?

Δx/y =voΔt + ½aΔt²

Which equation of uniformly accelerated motion is missing the "x/y" variable?

v = vo + aΔt

Which equation of uniformly accelerated motion is missing the "a" variable?

Δx/y = ½(vo + v)Δt

Which equation of uniformly accelerated motion is missing the "t" variable

v² = vo² + 2aΔx/y

How do you find the distance (in the y direction) when initial speed is 0 under constant gravity

Δy= 5Δt²

In free-fall and inclined-plane problems, what is the numerical relationship between drop time and drop distance?

When drop time is doubled, the drop distance increases by a factor of 4.

Provide the values of distance traveled and the speed after a particular time has passed in free fall situations (vo = 0) when t=1, t=2, t=3, t=4.

Which equation is used to determine distance? Which equation is used to determine the initial speed?
Which equation is used to determine time?

t=1; 5m; 10m/s
t=2; 20m; 20m/s
t=3; 45m; 30m/s
t=4; 80m; 40m/s

Δy= 5Δt²
V= Vo +gt

How would you use to determine the height of an apex during an object's flight with an initial speed of Vo?

Δy=Voy²/2g or Δy=Voy²/20

Explain the relationship between drag force and mass when comparing two objects of same volume but with different masses (solid vs hollowed).

The hollowed out ball is less massive and the magnitude of the drag force becomes comparable to its low weight. With a solid ball, the impact of wind resistance is trivial compared to its weight.

What is terminal velocity and its relationship with drag force. Also explain the relationships between the magnitude of terminal velocity, density, and contact area.

Greatest speed an object can reach. This occurs when acceleration acting on an object has a magnitude of 0, resulting from the magnitude of drag force perfectly offsetting the gravitational force in the opposite direction.

Greatest terminal velocity will be associated with the densest object having minimal contact.

Explain the motion of projectiles by breaking it into components

X and Y components can be treated separately. X-direction is subject to no acceleration (V=Vo; X=Vot), while Y-direction is subject to an acceleration of gravity (V=Vo +gt; Y=Vot+½gt² ). Whether or not an object is dropped or launched horizontally, when considering the Y-direction, the object is considered to start from rest. However, if an object is launched at an angle, the motion of the object must be broken down into X and Y components.

How can you divide the initial velocity into horizontal and vertical components?

Vox=Vo(cosθ)
Voy=Vo(sinθ)

How can you determine the range of a projectile where the initial height = final height?

r=2VoxVoy / g
r=Vo²Sin2θ / g

Maximum height of a projectile launched at 90 and 45 degrees. Also what is the relationship between maximum height and maximum range launched at 45 degrees?

when launched at 90 degrees, Hmax = h
when launched at 45 degrees, Hmax = h/2
when launched at 45 degrees, Rmax = 2h

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