Formulas

1. Convert the following to scientific notation in standard form.

a) 34674

b) 0.000235

2. Indicate the number of significant figures in each number.

a) 120000

b) 32100.0

c) 0.20040

3. Evaluate and use the correct number of significant figures in your answer.

a) 2.35cm x 4.6cm

b)

c) 2301cm +834.12cm +9.0cm

4. Rearrange the equation, solving for the variable shown (show all steps).

a) Solve for Q₁ where  

b) Solve for t where

c) Solve for v_o where

d) Solve for v_o where 

5. Solve the following triangle for R and θ using SOH CAH TOA and Pythagorus. Show all work.

R = ________________

θ = ________________

6. Unit conversions (show all work – lay out in brackets, same as lesson examples

a) 2.67 hours into seconds

b) 80 km/hr to m/s

c) 34 km into m

1. The acceleration of a freely falling object (near Earth), when we assume no air resistance, is _______________ (remember units).  This acceleration (due to gravity) is also called the __________________  ___________________ and is represented by the letter ________________.

2. The assumption of no air resistance is never totally true, but is often close enough to make pretty accurate calculations. Discuss cases where this is a really good assumption and when it isn’t.

3. A stationary boat accelerates to 90 km/hr over 1 km. What is the time it takes to do this?

4. A braking train can decelerate at 0.4 m/s^s. If the train is travelling at 160 km/hr and needs to plan to stop at a pick-up area. How far in advance does it need to apply the brakes?

5. A satellite in space is travelling at 14 m/s in one direction. A thruster is applied for 30 s and the satellite is then travelling at 12 m/s in the opposite direction. What acceleration does the thrust cause?

6. A rock is dropped off a 40 meter cliff. The rock accelerates due to gravity. What is the time it takes to hit the ground.

7. A motorcycle is travelling at a constant velocity of 90 km/h (no acceleration). How many seconds will it take the motorcycle to cover 2 km?

8. A stone is dropped from the top of a tall building. It accelerates at a rate of 9.81 m/s². How long will the stone take to pass a window that is 2.0 m high, if the top of the window is 20.0 m below the point from which the stone was dropped? HINT: draw a picture for starters. Show all work as demonstrated in the lessons.

9. Provide a description of a sample situation for each of the graphs below (make sure to recognize each graph as d vs t, v vs t, or a vs t.

10. To help you remember better, sketch a representation of the relationships between d vs t, v vs t, and a vs t graphs, in terms of slopes and areas.  (Note: FYI, this summary is the very basis of the study of Calculus.

1. Convert the following vector into vertical and horizontal components. Show all steps and include units.

2. Break the following vector into components (remember directions) – show work by sketching each vector, labelling the angle and showing components.

a) 25 [35° N of E]

3. Add the following vectors together using the component method.

                                                                                                                                                Sketch Resultant

X₁ = _________________      +   X₂ = ____________________      X_tot = __________________

Y₁ = _________________      +   Y₂ = ____________________      Y_tot = __________________

                                                                                                                                Magnitude of Resultant (hypotenuse)

                                                                                                                                R = ___________________

                                                                                                                                Direction of Resultant (hypotenuse)

                                                                                                                                θ = ___________________

4. A man walks 17m in a direction that is 20° N of E. He then changes direction and walks another 27m at 30° N of W. The two vectors are added together tip-to-tail as shown below. What is his overall displacement?

a) Determine the angle θ as shown above.

b) Draw in the resultant and label it R. Be sure to draw in the arrowhead to show its direction.

c) Using the Cosine Law, determine the magnitude of R. Show all work below.

5. Can three parallel vectors unequal in magnitude add to zero? Show with a vector diagram below.

6. Can three vectors of different magnitudes and directions add to zero.  Show with a vector diagram below.

7. Two swimmers of identical ability want to race across a river. The goal is to touch the other side first (anywhere along the bank). Both swimmers can swim at a rate of 5 m/s in still water. The river’s current is 3 m/s. Swimmer A points upstream so that she ends up travelling straight across the river along a line perpendicular to the point on the shore where she started. Swimmer B points directly across and ends up downstream due to the river’s current.

a) Which swimmer makes it across first?  Why do you think so?

b) If the river is 50m wide, determine the time it takes for each swimmer to cross.

c) How far downstream does Swimmer B end up?

8. An airplane travels with an airspeed of 400 km/h NE (in still air). Wind blows from the North at 50km/hr.

a) Break down both given velocities into components. Draw the original vectors roughly to scale and label the values of the x-y components directly on the sketch.

b) What component does wind affect? How does this affect the overall airspeed as seen from an observer on the ground? Remember “speed” is scalar. I am really asking if the plane speeds up or slows down overall.

c) What is the final velocity as seen from the ground? We call this v_g for velocity with respect to ground.

9. A jet aircraft is aimed south and travelling 851 km/hr. A wind blows the plane towards the east at 36.0 km/hr. What is the resultant velocity?

1. Describe (in your own words) what a projectile is. Provide examples.

2. What is the biggest difference in a projectile’s horizontal and vertical motion? What phenomenon causes this difference?

3. Summarize the (often) surprising result of shooting a gun and dropping a bullet at the same time. Why is this true (explain in terms of horizontal and vertical components of motion).

4. A boy throws a rock straight up into the air. Explain the changes taking place through the flight in terms of velocity and acceleration.

5. A stone is thrown horizontally at 15 m/s from the top of a cliff 44 m high.

a) How long does the stone take to reach the bottom of the cliff? Show all work as done in lessons.

b) How far from the base of the cliff does the stone strike the ground?  Show all work as done in lessons.

6. A golf ball is struck and leaves the ground at 48 m/s on a 60° angle.

a) How long will it be in the air before bouncing?

b) Determine the velocity of the ball 2 seconds after it was struck.

c) The most common incorrect answer for this question is 22m/s. What has actually been calculated if this is the answer?

7. What is the maximum height of a rock launched by a sling shot at 50 m/s on an angle of 80° ?

8. Find the range for a basketball thrown at 6.0 m/s at an angle of 50° above the horizon if it leaves from a height of 2.0 m.

9. During the filming of a TV show, a stuntman runs horizontally off the edge of the roof of a building 49 m high, with a horizontal velocity of 3.6 m/s.

a) For how many seconds will the falling stuntman be in the air?

b) How far out from the edge of the building should the safety bag be placed so that he can fall without being hurt?