Laws of motion and a projectile thrown from an accelerating elevator car

[Prabs3257]

Homework Statement

An elevator car starts descending with constant acceleration 2 m/s2 2 seconds after the start a ball is thrown horizontally with 3 m/s with respect to elevator from point P then the magnitude of displacement of the ball with respect to the point P after 1 second is

Relevant Equations

Projectile eqns

At the moment of throwing the ball the ball will have a vertical vel of 4 and horizontal of 3 wrt to elevator so as seen from inside the elevator the ball will behave like a projectile where g(eff) = 8 and with time period 1 sec hence range will be the displacement which should be 3 m but ans given is 5 m please tell me where i am wrong

 

[PeroK]

I suggest you use an inertial reference frame where both the elevator and ball are moving.

 

[Prabs3257]

I suggest you use an inertial reference frame where both the elevator and ball are moving.

But wouldn't it be easier to solve it from inside the elevator and use pseudo force am i doing the projectile path correctly

 

[PeroK]

But wouldn't it be easier to solve it from inside the elevator and use pseudo force am i doing the projectile path correctly

What does "horizontal" mean in this problem?

 

[Prabs3257]

i guess it means that if seen from inside the elevator it seems as if the ball is thrown horizontally

 

[PeroK]

i guess it means that if seen from inside the elevator it seems as if the ball is thrown horizontally

But, as the elevator and ball have different vertical accelerations that's not possible.

 

[Prabs3257]

But, as the elevator and ball have different vertical accelerations that's not possible.

but if we solve it from the elevator frame we can give that elevator's accel to the ball as pseudo force

 

[PeroK]

but if we solve it from the elevator frame we can give that elevator's accel to the ball as pseudo force

Okay, so how did you get an answer of 3m?

 

[Prabs3257]

so if we solve from the elevators frame ie make the elevator stationary the ball got a vertical vel of 4 and horizontal of 3 and by applying psudo force the net accel downward became 8 and time period came out to be 1 hence the displacement must be the range but my ans is not matching can you please tell me what i did wrong

 

[haruspex]

make the elevator stationary the ball got a vertical vel of 4

It says the ball is thrown horizontally relative to the elevator.
But it's not quite clear to me whether P is fixed in space or fixed to the elevator. You'd think it was fixed in space, but then I don't get any of the given answers.

 

[PeroK]

It says the ball is thrown horizontally relative to the elevator.
But it's not quite clear to me whether P is fixed in space or fixed to the elevator. You'd think it was fixed in space, but then I don't get any of the given answers.

Working backwards, I guessed they meant horizontal in the (moving, inertial) frame of the elevator at the time the ball was projected.

so if we solve from the elevators frame ie make the elevator stationary the ball got a vertical vel of 4 and horizontal of 3 and by applying psudo force the net accel downward became 8 and time period came out to be 1 hence the displacement must be the range but my ans is not matching can you please tell me what i did wrong

There shouldn't be an initial vertical velocity of $4m/s$. That would be a horizontal trajectory relative to the ground; not the elevator.

 

[Prabs3257]

It says the ball is thrown horizontally relative to the elevator.
But it's not quite clear to me whether P is fixed in space or fixed to the elevator. You'd think it was fixed in space, but then I don't get any of the given answers.

i got my ans by considering that p is in the elevator

 

[haruspex]

Working backwards, I guessed they meant horizontal in the (moving, inertial) frame of the elevator at the time the ball was projected.

Yes, that's what I wrote. My uncertainty concerns P.

 

[haruspex]

i got my ans by considering that p is in the elevator

Ok, so do that, but take the ball as being thrown horizontally relative to the instantaneous motion of the elevator.