Length Dilation and Projectile Motion Questions (1 Viewer)

[pokemonlv10]

Hey so this is from a past paper and I just can't figure out how to do it.

19) The rest length of a train is 200m and the rest length of a railway platform is 160m. The train rushes past the platform so fast that , when observed in the patform's frame of reference, the train and the platform are the same length.

How fast is the train moving?

a) 0.6c -> is the answer
b) 0.75c
c) 0.8c
d) 1.25c

20) A ball is launched horizontally from a cliff with an intial velocity of u m/s. After two seconds, the ball's velocity is in the direction 45 degrees from the horizontal. What is the magnitude of the velocity in m/s at 2 seconds?
a) u
b) 1.5u
c) 19.6
d) 27.7 -> is the answer

I've tried drawing them out, rearranging formulas bt i'm just not getting the answer.

 

[pikachu975]

For q19 just use the formula:
Lv = L0*sqrt(1-v^2 /c^2)
Sub Lv = 160 and then sub in the options for v and you find whichever one gets you L0 (200m) which is v = 0.6c.

 

[pokemonlv10]

Oh thanks you for question 19), i forgot that u can just use the answers from multiple choice and sub it in!

 

[pikachu975]

For q20:

let V be the speed at 2 seconds
let down be the positive direction

Vy = Vcos45

Sub this into Vy = Uy + at, Uy = 0 because there is no vertical velocity at the start
Vcos45 = 9.8(2)
V = 27.7 (D)

So I guess the initial information of u m/s is a distractor

 

[BenHowe]

It is launched horizontally, so initially you can consider it to be at it's turning point. Draw a diagram it helps visualise it