SPH 4UKinematics Review Problems

Concept Questions
  1. Draw the vector diagram illustrating how to find if you know and . Draw the vector diagram illustrating how to find if you were given and acceleration and time in 2-D.
  1. What does it mean to have a different frame of reference when dealing with relative motion?
  1. Why do airplanes usually take off and land into the wind, and not with the wind?
  1. Use vectors to explain why the relative velocity of a car is greater when it is coming directly at another car that is driving faster than the first, compared to when they are moving in the same direction.
  1. Write the general relative velocity equation to show air speed, ground speed, and speed relative to the air.
  1. Sketch the components of velocity and the instantaneous velocity vectors for a projectile at different points in time.

2-D and Projectile Motion Problems (FUNDAMENTALS OF PHYSICS – A Senior Course; p. 123)

  1. A batter strikes a baseball moving horizontally towards him at 15 m/s. The ball leaves the bat horizontally at 24 m/s, 40° to the left of a line from the plate to the pitcher. The ball is in contact with the bat for 0.01 s. Determine its average acceleration while being hit by the bat. (3.7 x 103 m/s2 [25 L of pitcher] - #35 b)
  1. A puck sliding across the ice at 20 m/s [E] is struck by a stick and moves at 30 m/s, at an angle of 120° to its original path. Find its change in velocity. (44 m/s [ S 53° W] - #34)
  1. An airplane flying at a constant speed of 1000 km/h executes a slow, level turn that changes its direction from west to east. If the turn takes 80 s, calculate the plane’s average acceleration in km/h/s. (25 km/h/s [E] - #31)
  1. A car accelerates from rest for 3.0 s at a rate of 2.4 m/s2. It then travels at a constant velocity for 6.0 s and finally decelerates at a constant rate over 5.0 s until it finally stops.

a)Draw a position : time graph that corresponds to this motion. Initial position is zero.

b)Draw the acceleration : time graph for this same motion.

  1. A dog walks at 1.6 m/s on the deck of a boat that is travelling north at 7.6 m/s with respect to the water.

(a)What is the velocity of the dog with respect to the waterif it walks towards the bow?

(b)What is the velocity of the dog with respect to the water if it walks towards the stern?

(c)What is the velocity of the dog with respect to the water if it walks towards the east rail, at right angles to the boat's keel? (9.2 m/s [N]; 6.0 m/s [N]; 7.8 m/s [N12E] - #22)

  1. An airplane is travelling 900 km/h in a direction 38.5° west of north.

a)Find the components of the velocity vector in the northerly and westerly directions.

b)How far north and west has the plane traveled after 3.00 h? (2113 km [N]; 1681 km [W])

c)Where is the plane relative to where it began after 3.00 h?(2700 km [N38.5W])

  1. A pilot wishes to fly straight to Toronto, which is 350 km [S 30°W] from Rolph International Airport. The plane flies at 200 km/h.

a)If there is a wind of 40 km/h blowing from the west, in what direction should he head?

b)How long will it take him to get there?(177 km/h [S40W]; 2 h)

  1. A newspaper boy throws papers sideways onto the porches of his customers while riding his bicycle along the sidewalk. The sidewalk is 15 m in front of the porches. The boy throws the papers at a horizontal speed of 6.0 m/s relative to himself, and rides the bicycle at a speed of 4.0 m/s relative to the sidewalk.

(a)With what horizontal speed do the papers actually travel relative to the ground?

(b)How far in advance of a porch should the boy throw a paper, so that it lands on target?

(c)If he waits until he is directly opposite a porch, at what horizontal angle with respect to the sidewalk will he have to throw the paper, to hit the porch?

(7.2 m/s; 10 m; 48 - #27)

  1. A bomber, diving at an angle of 53° to the vertical, releases a bomb at an altitude of 730 m. The bomb hits the gorund 5.0 s after being released. (p. 201 #45)

(a)What was the velocity of the bomber? (2.0 x 102 m/s)

(b)How far did the bomb travel horizontall during its flight? (8.0 x 102 m/s)

(c)Whate were the horizontal and vertical components of its velocity just before striking the ground? (1.6 x 102 m/s; 1.71 x 102 m/s)

  1. You are standing on top of the school with a snowball waiting to ambush your beloved physics teacher (must be a question from a different year). You are planning a high angle shot with an initial velocity of 20 m/s at 60°above the horizontal. The height of the school is 6.0 m.

a)What must be the horizontal displacement of your beloved physics teacher when you launch the snowball? (38 m)

b)What is the maximum height of the projectile above the launch level?(15.3 m)

c)With what velocity will the projectile impact?(22.4 m/s [63°below horizon])

  1. A bomber in level flight, flying at 92.0 m/s, releases a bomb at a height of 1950 m.

(a)How long is it before the bomb strikes the Earth?

(b)How far does it travel horizontally?

(c)What are the horizontal and vertical components of its velocity when it strikes?

(d)What is its velocity of impact?

(19.9 s; 1.84 x 103 m; 92.0 m/s, 195 m/s; 216 m/s [64.7° below the horizontal] – p. 174 #5)

SIN QUESTIONS(Tough but do-able)

  1. A person walks up a stalled escalator in a department store in 90 s. When standing still on the same escalator in motion, he is carried up in 60 s. How much time would it take him to walk up the moving escalator? Could he walk down the escalator while it was moving up? If so, how long would that take? (SIN '70) (36 s, no - #42)

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