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

In summary: Yes, that's what I wrote. My uncertainty concerns P.Ok, so do that, but take the ball as being thrown horizontally relative to the instantaneous motion of the elevator.
  • #1
Prabs3257
65
4
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
 

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  • #2
I suggest you use an inertial reference frame where both the elevator and ball are moving.
 
  • #3
PeroK said:
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
 
  • #4
Prabs3257 said:
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?
 
  • #5
i guess it means that if seen from inside the elevator it seems as if the ball is thrown horizontally
 
  • #6
Prabs3257 said:
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.
 
  • #7
PeroK said:
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
 
  • #8
Prabs3257 said:
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?
 
  • #9
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
 
  • #10
Prabs3257 said:
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.
 
  • #11
haruspex said:
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.

Prabs3257 said:
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.
 
  • #12
haruspex said:
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
 
  • #13
PeroK said:
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.
 
  • #14
Prabs3257 said:
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.
 

1. What are Newton's Laws of Motion?

Newton's Laws of Motion are three physical laws that describe the relationship between an object's motion and the forces acting on that object. The first law states that an object at rest will remain at rest and an object in motion will remain in motion at a constant velocity unless acted upon by an external force. The second law describes how the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The third law states that for every action, there is an equal and opposite reaction.

2. How do Newton's Laws of Motion apply to a projectile thrown from an accelerating elevator car?

When a projectile is thrown from an accelerating elevator car, all three of Newton's Laws of Motion apply. The first law applies because the projectile will continue moving in a straight line at a constant speed unless acted upon by a force, such as gravity or air resistance. The second law applies because the net force acting on the projectile (gravity) will cause it to accelerate downwards. The third law applies because the projectile exerts an equal and opposite force on the elevator car as it is thrown.

3. How does the acceleration of the elevator car affect the projectile's motion?

The acceleration of the elevator car will affect the projectile's motion by changing its initial velocity. If the elevator car is accelerating upwards, the projectile's initial velocity will be greater than if the elevator car was at rest. This will result in a longer flight time and a higher maximum height for the projectile. If the elevator car is accelerating downwards, the projectile's initial velocity will be lower, resulting in a shorter flight time and a lower maximum height.

4. How does air resistance affect the motion of a projectile thrown from an accelerating elevator car?

Air resistance will have a greater effect on the motion of a projectile thrown from an accelerating elevator car compared to one thrown from a stationary elevator car. This is because the projectile will be moving at a higher initial velocity due to the elevator's acceleration, making it more susceptible to the opposing force of air resistance. Therefore, the projectile will experience a shorter flight time and a lower maximum height due to the air resistance slowing it down.

5. How can we calculate the trajectory of a projectile thrown from an accelerating elevator car?

To calculate the trajectory of a projectile thrown from an accelerating elevator car, we can use the equations of motion, which are derived from Newton's Laws of Motion. These equations take into account the initial velocity, acceleration, and time to calculate the projectile's position at any given time. We can also consider external forces such as air resistance to make the calculation more accurate. Additionally, we can use computer simulations to model the projectile's motion and accurately predict its trajectory.

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