SUVAT equations + two balls dropped at different times

In summary, the SUVAT equations assume that t = 0 when motion starts and uses separate clocks for each mass's motion. The time for the first ball, t, is equal to the time for the second ball, t+1, plus the time interval between the two motions, t0. Therefore, t-1 is the correct time for the second ball, not t+1.
  • #1
trew
19
0
Homework Statement
two balls dropped
Relevant Equations
suvat
I'm continuing to struggle when it comes to objects that are dropped at different times.

At height h, a ball is dropped at rest.

Also at height h, another ball is dropped one second later.

For the first ball, time=t.

For the second ball, time=t+1...but this is wrong? The answers show it should be: t-1. How?

If I drop ball right now, then the time is t, and if I drop a second ball one second later, then isn't the time t+1?
 
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  • #2
The SUVAT equations assume that t = 0 when motion starts. Imagine two separate clocks, 1 and 2. Each clock starts when its corresponding mass starts its motion. Write the SUVAT equations as usual using t1 and t2. The latter clock 2 will be behind clock 1 by t0, the time interval between the onset of the two motions. Therefore t1 = t2 + t0 because t1 is a greater number than t2.
 

1. What are SUVAT equations?

SUVAT equations are a set of equations used in physics to describe the motion of an object in terms of its displacement (S), initial velocity (U), final velocity (V), acceleration (A), and time (T). These equations only apply to motion with constant acceleration.

2. How are SUVAT equations used in analyzing the motion of two balls dropped at different times?

In the case of two balls dropped at different times, SUVAT equations can be used to calculate the position, velocity, and acceleration of each ball at any given time. This allows us to compare the motion of the two balls and determine how they are affected by factors such as gravity and air resistance.

3. Can SUVAT equations be used to analyze the motion of objects with non-constant acceleration?

No, SUVAT equations only apply to motion with constant acceleration. For objects with non-constant acceleration, more complex equations, such as those derived from calculus, must be used.

4. How do the initial conditions affect the motion of the two balls?

The initial conditions, such as the initial velocity and position, will determine the motion of the two balls. If the two balls are dropped from the same height but with different initial velocities, the ball with the higher initial velocity will reach the ground first. If the two balls are dropped with the same initial velocity but from different heights, the ball dropped from the higher height will reach the ground first.

5. Is it possible for the two balls to reach the ground at the same time?

Yes, it is possible for the two balls to reach the ground at the same time if they are dropped from the same height and at the same time. This is because the acceleration due to gravity is the same for both balls, so they will experience the same rate of change in velocity and reach the ground at the same time.

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