To** decrease **a value by the percentages listed below, you would

Multiply Original by _______ (in decimal and in fraction):

20%, 25%, 33%, 50%, 67%, 75%, 80%, 100%

To __ raise__ a value by the percentages listed below, you would

Multiply Original by _______ (in decimal and in fraction):

20%, 25%, 33%, 50%, 67%, 75%, 80%, 100%

Given the equation vf = (2gh_{i})^{1/2}, by what factor does the final velocity change if the initial height is increased by a factor of 4?

A. Increase by factor of 2

B. Increase by factor of 4

C. Decrease by factor of 2

D. Decrease by factor of 4

__h _{i} goes up by 4__

v_{f }œ [h_{i}]^{1/2}

v_{f}^{2 } œ [h_{i}]

(up by 2) (up by 4)

**A. Increase by factor of 2**

Given the equation v_{f} = (2gh_{i})^{1/2}, by what factor did the initial height change if the final velocity was increased by a factor of 4?

A. Increase by factor of 2

B. Increase by factor of 4

C. Decrease by factor of 2

D. Decrease by factor of 4

__ v _{f} œ (h_{i})^{1/2}__

v_{f}^{2} œ h_{i}

(up by 4) (up by 16)

**D. Increase by factor of 16**

Given the equation F = GMm/r^{2}, by what percent does the force change if the distance is increased by a factor of 2?

A. Decrease by 25%

B. Decrease by 75%

C. Decrease by 100%

D. Decrease by 300%

__F æ 1/r ^{2}__

r goes up by 2

F goes down by 4

F_{i }x 1/4 *(You keep 25% so only have 75% left)*

**B. Decrease by 75%**

Given the equation F = GMm/r^{2}, by what percent does the force change if the distance is decreased by a factor of 2?

A. Increase by 25%

B. Increase by 200%

C. Increase by 300%

D. Increase by 400%

F œ 1/r^{2}

r goes down by 2

F goes up by 4

F_{i} x 4

Check: F_{i} = 100, F_{f} = 400: %= (400-100)/100 x 100 = 300%

% Change = (F_{f} - F_{i})/F_{i}

What are the fractions for Sin(θ) and Cos(θ)?

For (θ) = 0°, 30°, 45°, 60°, 90°, 180°, 270°

What are the areas and volume formulas for spheres and cylinders?

What are the areas and volume formulas for triangles and rectangles and squares?

Define y= log [X]

and y=ln (X)

Given that PV = nRT, if the pressure is held constant which graph represents the relationship between temperature and volume?

Given that PV = nRT, if the pressure is held constant what graph represents the relationship between temperature and volume?

Given that PE = -Gmm/r, which of the following graphs represents the relationship between PE and r?

Which of the following graphs demonstrates an object in free fall? (Assume g = 10 m/s^{2})

How would a graph demonstrate an object moving at a constant positive velocity?

*x-axis: t*

*y-axis: d*

4 Steps to Picking the Right Graphs

**RECALL: y=mx +b**

1) Write an equation from graph.

2) Write what's on the x and y-axis.

3) Group together the terms and rearrange to solve for y.

4) Substitute variables given for m, x, and y.

- If y=constant/x: parabolic
- If y = m x: linear.
- Assign +/- slope based on question context.

What graph correctly depicts v vs t for an object dropped from rest?

(Assume g = 10 m/s^{2)}

x-axis: t

y-axis: v

Slope = acceleration

Which of the following graphs correctly depicts vy vs t for a projectile thrown vertically upward?

(Assume g = 10 m/s^{2})

x=v

y=t

Kinematics Equations

A rock is dropped from a cliff that is 100 m above ground level. How long does it take the rock to reach the ground? (Note: Use g = 10 m/s2)

A) 4.5 s

B) 10 s

C) 14 s

D) 20 s

Equation: XAT

Starting from a resting position, a certain toy catapult applies a constant force of 3.0 N to

a projectile with a mass of 0.06 kg. How long will it take for the projectile to move 1.0 m?

A) 0.02 s

B) 0.04 s

C) 0.20 s

D) 0.40 s

Equation: TAX

In the absence of air resistance, what maximum height will be reached by a 5-kg

projectile with an initial vertical speed of 50 m/s? (Note: Use g =10 m/s2.)

A) 25 m

B) 50 m

C) 125 m

D) 250 m

Suppose that a ball is thrown vertically upward from earth with velocity v, and returns to its original height in a time t. If the value of g were reduced to g/6 (as on the moon), then t would:

A) increase by a factor of 6.

B) increase by a factor of 6^{1/2 }

C) decrease by a factor of 6.

D) decrease by a factor of 6^{1/2 }

Two identical projectiles are given the same horizontal speed, but one is launched horizontally while the other is launched at an angle of 10° above the horizontal. If the projectiles do NOT experience air resistance, how will their time spent in flight and horizontal distance traveled compare?

A) The horizontal projectile will travel farther and be in the air longer.

B)The horizontal projectile will travel the same distance but will be in the air a shorter amount of time.

C) The horizontal projectile will travel less distance but will be in the air longer.

D) The horizontal projectile will travel less distance and be in the air a shorter amount of time.

Two projectiles are propelled with the same initial vertical speed but with different initial horizontal speeds. If air resistance is negligible, how will their time in the air and horizontal flight distance compare?

A) They will remain in the air different amounts of time but travel the same distance.

B) They will remain in the air different amounts of time and travel different distances.

C) They will remain in the air the same amount of time and travel the same distance.

D) They will remain in the air the same amount of time but travel different distances.

Newton's First Law

Trigonmetric Relations