Speed - the bus jump in the movie

[Phalon88]

Speed --- the bus jump in the movie!

Homework Statement

In the movie Speed1, a loaded city bus is rigged with an explosive that will detonate and kill everyone aboard if its speed goes below 50 miles per hour. As the bus is moving, the people on board are informed that a bridge ahead in the highway they are on is still under construction and is missing a center segment. They can’t slow down so decide to jump it, so they begin to accelerate.



You must watch a film clip below from the movie to get a good overview of the problem at hand. Some information you need is given in the clip also (observe and listen).

It is then up to you to determine, given the information you hear and observe, if their plan will work.



Q1. Just before the jump, using the info you have and projectile motion (i.e. no air friction) with simple calculations, where would bus be once it reaches other side of unfinished section of bridge (also include a trajectory diagram)?



Q2. What’s about the jump scene is not consistent with the previous scenes?



Q3. Given the info you have, what would be the minimum velocity (magnitude and direction) required to make that jump (include another trajectory diagram and clearly show your calculations)?



Q4. What about the bus might lead you to alter your answers to Q3 a bit for a safe landing?


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Homework Equations

Vy = Voy + aT ... Vx = Vox + aT
delta y = VoyT + 1/2aT^2 ... Delta x = VoxT + 1/2at^2
delta y = 1/2(voy + Vy)T ...Deta x - 1/2 (vox + Vx)T
Vy^2 = Voy^2 + 2a(delta) ...Vx^2 = vox^2 + 2a(deltax)

The Attempt at a Solution

delta x = 50 ft = 15.24 m
To find T I used V = (delta x)/(delta t)
29.78 m/s = (15.24 m)/t
t=0.511 s
I then used the formula:
delta y = VoyT + 1/2aT^2
I knew that Voy = 0, a = -9.8 m/s^2
so I got -1.279 m = delta y.
So from the negative I know that the bus fell DOWN. so there is no way it made the jump without crashing. If it was > 0 it would have made it just fine.

I'm stumped for question 3...
I have all my components 'figured' out:
Y axis:
Voy = 0 m/s
Ay = -9.8 m/s^2
delta y = -1.279m
T = 0.511s

x axis:
Vox = Vx = 29.78 m/s
Ax = 0
delta x = 15.24 m
T = 0.511 m

I really need help with this. thanks

 

[willem2]

There should be an upslope, so the initial velocity in the y direction is not 0. No value for the angle of the slope is given, but you can work out the minimum value from the speed of the bus and the size of the gap,

 

[Phalon88]

How?
Do you mean I calculate the min velocity needed using the speed and distance of gap?
Or do you mean the angle?
I can't figure out how to solve the angle to get initial V in the y direction, because then I wouldn't know delta y and therefore would only know one side of the triangle --> delta x?