Solve Kinematics Problem: Ball Thrown Upward in Elevator

In summary, the conversation discusses a problem involving a ball being thrown upward in an elevator traveling at 10m/s. The ball's speed is 20m/s and the question is how long it takes for the ball to reach the same point it was thrown from. The suggested solution is to use Galilean transformations and solve for the time by setting the positions of the elevator and ball equal to each other.
  • #1
Nenad
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hi guyes, I was wondering if someone could help me with a problem I had on a quiz. The question he's been puzzeling me for some time now.

A ball is thrown upward in an open roof elevator traveling at 10m/s(elevator speed). The balls speed is 20m/s. How much time does it take for the ball to reach the same point it was thrown at?
 
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  • #2
You could use galilean transformations to solve this one, the 10m/s of the elevator must be relative to a inertial frame observer, as the 20m/s. Find the speed relative to the elevator, to simplify calculations.
 
  • #3
Nenad said:
A ball is thrown upward in an open roof elevator traveling at 10m/s(elevator speed).
Is the elevator rising or falling?
The balls speed is 20m/s.
I assume that's the ball's speed with respect to the earth/elevator shaft.
How much time does it take for the ball to reach the same point it was thrown at?
I assume you mean same point with respect to the elevator car?

Find the position of the elevator car as a function of time. (Constant speed.)
Find the position of the ball as a function of time. (Constant acceleration.)

Set them equal and solve for the time.
 

FAQ: Solve Kinematics Problem: Ball Thrown Upward in Elevator

How does the motion of a ball thrown upward in an elevator differ from that in free fall?

The motion of a ball thrown upward in an elevator will be affected by the acceleration of the elevator, while a ball in free fall will only be affected by the acceleration due to gravity.

What is the equation for the position of the ball in this scenario?

The equation for the position of the ball can be written as s(t) = s0 + v0t + 1/2at^2, where s0 is the initial position, v0 is the initial velocity, a is the acceleration, and t is time.

How does the acceleration of the elevator affect the motion of the ball?

If the elevator is accelerating upwards, the ball will experience a greater acceleration and will rise faster. If the elevator is accelerating downwards, the ball will experience a smaller acceleration and will fall slower.

Can the ball reach its maximum height if the elevator is accelerating downwards?

No, the acceleration of the elevator will act against the motion of the ball and it will not be able to reach its maximum height. The maximum height can only be reached if the elevator is either stationary or accelerating upwards.

How can we calculate the maximum height reached by the ball in this scenario?

The maximum height can be calculated by setting the velocity of the ball to zero and solving for the time. This time can then be substituted into the equation for position to find the maximum height.

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