Discussion Class 1 (Ch2)
Questions
Q9)A cream tangerine is thrown directly upwards past three evenly spaced consecutive e windows of equal height as shown alongside. Rank the windows (greatest first) according to the median speed of the cream tangerine while passing through them, the time taken to pass through them, the magnitude of the median acceleration while passing through them, and the change in speed during the passage through them.
Median speed: 3,2,1 as cream tangerine travels higher, since it is a projectile it will slow down since velocity and acceleration are in opposite directions
Time: 1,2,3 distance is same through each window thus one with greatest median speed will have the smallest time
Acceleration: 1=2=3 all projectiles have the same acceleration regardless of position or time
: 1,2,3 thus greater time implies greater
Problems
P18)The position of a particle moving along an x axis is given by , where x is in metres and t is in seconds.
a)Determine the position, velocity and acceleration at 3s.
b)What is the maximum positive position reached by the particle and what time does it reach this position?
c)What is the maximum positive velocity reached by the particle and what time does it reach this velocity?
d)What is the acceleration at the instant the particle is not moving (other than at t=0 s)
not movingas per (b)
e)Determine the average velocity of the particle between 0 s and 3 s
P45)With what velocity must a ball be thrown vertically into the air if it is to reach a maximum height of 50 m above the release point? How long is it in flight when it reaches this maximum height?
P78) A red train travelling at 108 km/h and a green train travelling at 144 km/h are headed towards each other along a straight, level track. When they are 950 m apart, each engineer sees the other train and applies the brakes. The brakes slow each train at a rate of 1.0 m/s2. Is there a collision? If so, answer yes and give the velocity of each train at impact. If not, answer no and give the separation between the trains when they stop.
Assume the trains collide:
Red train:
Green train:
Red train:
Green train:
Discussion Class 2 (Ch4)
Questions
Q8) A ball is thrown up past windows 1,2, and 3, which are identical in size and regularly spaced vertically. After reaching its maximum height, the ball then moves down past windows 4,5, and 6 which are identical in size but irregularly spaced horizontally. A diagram of this situation is shown below
a)Rank the first three windows according to the time taken for the ball to pass the window. Explain
3,2,1 ball passes from bottom to top of window (vertical motion) thus same reason as for DC1 Q9
b)Rank the second three windows according to the time taken for the ball to pass the window. Explain
4=5=6 ball passes from left to right of the window (horizontal motion) and hence since we only look at x-direction and x-direction velocity is constant then ball takes same time to pass through each window
c)Rank the six windows according to the magnitude of the acceleration experienced by the ball. Explain
All same. Projectiles all have the same constant acceleration with magnitude 9.8 m/s2 and that does not change during motion
Problems
P11) The position of a particle moving in an xy plane is given by .
a)In unit vector notation find , and for t=2.00 s
b)What is the angle between the positive x axis and a line tangential to the path of the particle at t = 2.00 s?
line tangential to the path of the particle=velocity vector
P27) A certain airplane has a speed of 290.0 km/h and is diving at below the horizontal when the pilot releases a radar decoy. The horizontal distance between the release point and the point where the decoy strikes the ground is d=700 m
a)How long is the decoy in the air?
b)How high is the release point above the ground?
Release point is 897 m above ground
P32 continued) Look at the sample problem again:
b)What are the vertical and horizontal components of the velocity of the ball when it hits the wall?
Vertical:
Horizontal:
c)When it hits the wall has it passed its highest point on its trajectory?
No. The velocity in the y direction is positive hence it is still travelling upwards thus cannot yet have reached its maximum height
Discussion Class 3 (Ch4)
Questions
Q13)
a)Is it possible to be accelerating while travelling at constant speed? Explain
Yes. If acceleration is perpendicular to velocity then it will change velocity’s direction but not its magnitude (e.g. circular motion)
b)Is it possible to round a curve with zero acceleration? Explain
No. In order to change direction of velocity there must be an acceleration, otherwise object would carry on going straight
c)Is it possible to round a curve with a constant magnitude of acceleration? Explain
Yes e.g. circular motion accelerations magnitude is constant provided that speed and radius of curve is constant
Problems
P35)A rifle that shots bullets at 460 m/s is to be aimed at a target 45.7 m away. If the center of the target is level with the rifle, how high above the target must the rifle barrel be pointed so that the bullet hits dead centre?
Consider motion of projectile till halfway point (i.e. maximum height), let
x- direction:
y-direction:
P58)A rotating fan completes 1200 revolutions every minute. Consider the tip of a blade, at a radius of 0.15 m.
a)Through what distance does the tip move in one rotation?
b)What are the magnitudes of the tips velocity and acceleration?
P108) The Gautrain has a required average speed of 160 km/h
a)If the train goes around a curve at that speed and the magnitude of the acceleration experienced by the passengers cannot exceed 0.050, then what is the smallest radius of curvature for the track that can be tolerated?
b)At what speed must the train go around a curve with a 1.00 km radius to be at the acceleration limit?