Post by: /0 on May 21, 2008, 07:32:16 pm
A runner finishes a 35m race at a speed of 12m/s. He ran with a constant positive acceleration throughout the race of 2m/s. What was the shortest time he could have spent running the race?
(a) 4.0s
(b) 5.0s
(c) 6.0s
(d) 7.0s
What was his average speed for the race?
(a) 4.0m/s
(b) 5.0m/s
(c) 6.0m/s
(d) 7.0m/s
Two superheroes have the unique property of colliding elastically with everything they run into. They run headlong into each other. Before the collision, one is travelling with a speed of 100m/s East; the other is travelling at a speed of 150m/s West. When they rebound, the heavier one is travelling at 50m/s. Which two of the following are possible ratios of the masses of the two superheroes?
(a) 2:1
(b) 7:3
(c) 3:2
(d) 9:4
Hiawatha fires an arrow into the air with a speed of 60m/s. He can run at 30m/s. Legend has it that he could fire an arrow and then catch it at the end of its flight (on level ground). Which of the following is closest to the angle to the horizontal he must have fired it at? (Of course you can neglect things like air resistance and the time it takes him to start running after firing the arrow!)
(a)
(b)
(c)
(d)
The speed at which grass grows in spring (in Melbourne) is closest to:
(a)
(b)
(c)
(d)
Post by: cara.mel on May 21, 2008, 11:00:22 pm
1.
x = 35
a = 2
v = 12
t = ?
x = vt - .5at^2
35 = 12t - t^2
t^2 - 12t + 35 = 0
(t-7)(t-5) = 0
t = 5 or t = 7
Question asks for shortest time => he didnt spend a second running the wrong way => 5s
2. Assuming this carries on from Q1 and he doesnt decide to take 7s
Initial speed = 2m/s
Final = 12
average = 7
3. I can't be bothered, too tired will do tomorrow =)
conservation of energy + momentum, usually physics questions dont require thinking :( Although it looks very fun :D
4. I feel I've missed something... just want horizontal component of velocity to be 30, but then theta = 60. =/
5. In spring, Mel's house's lawn needs to be mowed once every week. In each week it grows maybe 3cm (Mel is not sure as she doesn't do it, but for order of magnitudes idc)
Therefore, it grows 0.03m in 604800s
Therefore, ~4.5*10^-8/s
Therefore, I can't estimate very well Grass Growing Time as I am in between two options
Therefore, we must conclude that d is right and that the grass grows 10 centimetres per second.
Post by: Mao on May 22, 2008, 01:20:04 am
5. In spring, Mel's house's lawn needs to be mowed once every week. In each week it grows maybe 3cm (Mel is not sure as she doesn't do it, but for order of magnitudes idc)WOAH MAGICAL BEANSTALK
Therefore, it grows 0.03m in 604800s
Therefore, ~4.5*10^-8/s
Therefore, I can't estimate very well Grass Growing Time as I am in between two options
Therefore, we must conclude that d is right and that the grass grows 10 centimetres per second.
and for Q4, if the trick is in "closest", I pick [A] =]
Post by: cara.mel on May 22, 2008, 02:28:00 pm
First use conservation of energy to establish that the lighter one is going at 200m/s after the collision
Then use conservation of momentum for both scenarios:
Scenario A: Heavy is initially going at 100m/s E, final at 50m/s W | light initial = 150 W, final = 200 E
Scenario B: Heavy is initially going at 150m/s W, final at 50m/s E | light initial = 100 E, final 200 W
When you do both of those you get a ratio of m1:m2, which are 7/3 and 3/2 in the order in which I wrote them => B and C
Post by: /0 on May 22, 2008, 05:39:21 pm
With the firing arrow one I also get 60 degrees, and although 58 degrees is the closest, that's not quite accurate enough, because it will mean he will not run fast enough to catch it. Then again, if you choose 63 degrees, he will overrun the arrow, but considering practicalities, he could simply slow down and catch it. Difficult question huh? :P