Physics Question. Kinematics in 1 Direction?

Question

I'm having trouble with this concept question:

Two objects are thrown vertically upward, first one, and then, a bit later, the other. Is it possible that both reach the same maximum height at the same instant? Account for your answer.

I'm implying that there is gravity, these are basic objects that can't propel themselves, and that air resistance is ignored. But I can't be completely sure about all of that.

Answer 1

Yes, definitely ...

The second one will have to be thrown at a higher speed than the first one.

For an object thrown vertically upward, the working formula is

S = VT - (1/2)gT^2

where

S = maximum height that the object will attain

V = initial velocity at which it was thrown

T = time

g = acceleration due to gravity (constant value of 9.8 m/sec^2)

For the first object, maximum height reached = S1 and for the second object, maximum height = S2. Since the problem stipulated that both reached the same maximum height, then

S1 = S2.

For the first object, the time it took to reach maximum height is T1 and for the second object, the time it took to reach maximum height is T2.

Since T2 > T1, then the only obvious factor that will make S1 = S2 is that V2 (velocity of the second object) is higher than V1 (velocity of the first object).

Answer 2

Te maximum height is (v(initial)^2)/(2g).

By delaying the release of the second object, you will have to increase v(initial) so that the same point in the curve is reached, but doing so will increase the maximum height as well.

The only way to compensate is by adjusting both the initial displacement(distance from ground) and the initial velocity of the second object.