Which Brick Lands with the Highest Speed and Other Physics Enigmas?

[lollol]

1) Three bricks are thrown from the roof of a building with the same speed but with different launch angles: one above the horizontal, one below the horizontal and one horizontal. Assuming no air resistance, which brick has the highest speed by the time it reaches the ground?

My answer: Simple conservation of energy... mgh = 0.5mv^2. They all have the same velocity... is this correct? Just wanted to confirm

2) If 2 cars crash, which would you expect to be more harmful to the passengers: if the cars crash and stay together, or if the cars collide and rebound backward? Explain.

My answer: Honestly, I am not sure at all. Momentum is conserved in both, thus impulse is 0. Only thing is... energy is lost in a sticky collision, so I'm going with an inelastic collision. However, I cannot explain it.



3) Can the total mechanical energy be negative? E = KE + PE
Explain + provide an example.

My answer: I always learned that energy is positive. But I'm thinking this can depend on the point of reference. If my reference point is 1000m above a cliff, the potential energy of a rock on the cliff is negative and has no kinetic energy... so E is -ive.

 

[Dick]

For 2) what's harmful to the passengers is the acceleration. Assuming both collisions happen in the same time t at the same velocity v, then in one case they decelerate from v to 0 in time t. In the other they decelerate from v to 0 and then up to the rebound velocity in the same time. In which case is the magnitude of the acceleration larger? 1) looks fine. And yes for 3). KE is positive but PE depends on a choice of origin and can certainly be negative.

 

[lollol]

For 2) what's harmful to the passengers is the acceleration. Assuming both collisions happen in the same time t at the same velocity v, then in one case they decelerate from v to 0 in time t. In the other they decelerate from v to 0 and then up to the rebound velocity in the same time. In which case is the magnitude of the acceleration larger? 1) looks fine. And yes for 3). KE is positive but PE depends on a choice of origin and can certainly be negative.

So in fact, the total mechanical energy can be negative then... it all depends on the magnitude of the values?

 

[Dick]

So in fact, the total mechanical energy can be negative then... it all depends on the magnitude of the values?

Sure. PE can be negative, so if it's magnitude is greater than KE, the total is negative.