BR Physics Chapter 1, Passage V

[jillzhou]

I've been getting these types of questions wrong and was hoping someone would clarify this:
(It's passage 5 questions 30 and 33 from the first chapter of TBR Physics). I understand that the cannon balls would reach the ground in the following order: red, white and blue but then why does the answer key say the white ball has a longer range than the blue one. Assuming the white one reaches the ground first, wouldn't it have a smaller range?

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[Gauss44]

Trajectory. The 60 degree angle produces a trajectory with a greater arch sacrificing range. If using X=Vo*T, remember to multiply Vo by the cos of the launch angle. Cosine of 60 degrees = .5 est.; cosine of 30 degrees = .9 est.

 

[Deadlifts]

I've been getting these types of questions wrong and was hoping someone would clarify this:
(It's passage 5 questions 30 and 33 from the first chapter of TBR Physics). I understand that the cannon balls would reach the ground in the following order: red, white and blue but then why does the answer key say the white ball has a longer range than the blue one. Assuming the white one reaches the ground first, wouldn't it have a smaller range?

I googled the problem since you didn't include it in the post. Hopefully this is the right one.
"A cannon is located on the edge of a cliff 100 m above a flat, sandy canyon floor. three cannon balls are launched from the cannon with the same initial speed of 50m/sec but at different angles. the cannon balls are identical except for their color. a red ball launched horizontally. white ball launched at 30degrees above horizontal. blue ball launched 60 degrees above horizontal.

If it were possible to launch all three cannon balls simultaneously, which order would they hit the ground? "

Range is referring to the X distance travelled. Remember that they're giving you 3 velocities, 2 of which have X and Y components. It doesn't really require you to calculate anything if you understand how a steeper angle would yield a greater |Vy| and smaller |Vx| . The quicker you can visualize, avoid lengthy calculations and still answer correctly, the better you'll do on the actual test.

While the white ball may hit the ground before the blue ball, range depends on how fast it is travelling in the x-direction.

 

[peacefulheart]

I've been getting these types of questions wrong and was hoping someone would clarify this:
(It's passage 5 questions 30 and 33 from the first chapter of TBR Physics). I understand that the cannon balls would reach the ground in the following order: red, white and blue but then why does the answer key say the white ball has a longer range than the blue one. Assuming the white one reaches the ground first, wouldn't it have a smaller range?

1. This is a hard passage. Background information: A football team is holding tryouts for place-kickers. A place-kicker's job is to kick the football from the ground so that it travels in a trajectory that allow its to clear a horizontal bar........

2. #30, In presence of air resistance, which following statement is true about the flight of the football.

A. The range remains the same, the time of flight decreases.
B. The range remains the same, the time of flight increases.
C.The range decreases, the flight of time remains the same.
D. The range increases, the flight of time remains the same.

The answer is C.
In terms of range ( R=Vox*t, ), if there is no air resistance, the Vox*t (horizontal velocity) will not change as a constant. With air resistance, the horizontal velocity decreases with time, thus, range decrease with time. The point to remember is that air resistance also affect horizontal velocity.

In terms of maximum height , without air resistance, it is h=(Voy*)^2/2g ;with air resistance, it is h=(Voy)^2/2a. Here a is bigger than g since when the football is up, mg +f (air resistance)=ma. So, with air resistance, the football will not go the same height as it would be without air resistance. By common sense, when air resistance and gravity both work in the same direction (down), it is obvious that the football will achieve a lower height.

In terms of flight of time, without air resistance, the time for the up trip will be the same as the time down trip. With air resistance, air resistance affects the up trip and down trip differently since mg+f=ma for up trip and mg-f=ma for down trip. Namely, for the up trip, air resistance helps to reduce the flight time while for the down trip, air resistance tends to increase the flight of time. Here comes to be controversial:
According to EK book, the air resistance affect fast-moving objects more , so the air resistance reduce the up trip more than it increase the down trip in terms of time. Therefore, the overall flight of time will be less.
According to TBR book, the time decreased in the up trip is cancelled out by the time increased during the down trip. Therefore,the overall time remains the same.

I hope somebody can clear this off.

3.#31. All of the following statements about the kicking of the football and its flight are true EXCEPT.
A it is best if the football has a vertical velocity in the downward direction as it crosses the horizontal line.
B. The mass of the football does not affect its range.
C. The football changes direction throughout its flight.
D. The horizontal velocity of the ball is affected by air resistance.

The answer is B.

A is true because when the football has downward vertical velocity , the football moves further horizontally compared with only upward vertical velocity ( draw a projectile motion graph). When the football moves further horizontally, it easier for it to clear the horizontal bar.

B is not true because the mass of the football does affect its range by affecting its initial velocity. From the conservation of energy, the energy from the foot of the kicker is transferred to the kinetic energy of the football. Assuming the energy from the foot of the kicker is the same all the time, the kinetic energy , which is equal to 1/2mv^2, is also the same all the time. So, when m is larger ( a heavier ball), v (initial velocity) is smaller. By common sense, it is easier to kick to lighter ball than heaver ball.

C is obviously true.
D is true as explained in the #30.

4.# 32. During two separate field goal attempts, the kicker kicks the football with same horizontal speed but with a larger vertical speed on the second kick.The kicker made this change most likely because on the second kick, the goal posts were:

A. farther away, but the kicker wanted the same flight.

B. the same distance away, and the kicker wanted the ball to reach a lower maximum height.
C. farther away, and the kicker wanted a longer flight time.

D. Closer, and the kicker wanted a smaller launch angle.

The answer is C.
Remember, the first part of each answer can not contradict the second part of the answer in order for the answer to be right.

Think about this way, what does vertical velocity affect? It affects the maximum height and the flight time. The larger the vertical velocity, the larger the maximum height, and the longer the flight time (h=at), the greater the range ( horizontal velocity remains the same). That means the second time, the goal posts were far away( greater range), and a longer flight time.

thanks

 

[dbouz]

I'm confused. Wouldn't the range be equal? Blue has a smaller Vx but it also has a bigger time of flight. So wouldn't it all come out to the same range in the end?