Collision of baseball with falling person

[negation]

Homework Statement

You throw a baseball at a 45 degrees angle to the horizontal, aiming at a friend who's sitting in a tree a distance, h, above ground. At the instant you throw your ball, your friend drops another ball.

a) Show that the two balls will collide, no matter what your ball's initial speed, provided it's greater than some minimum value.
b) Find an expression for that minimum speed.

The Attempt at a Solution

Am I expected to provided an arbitrary initial velocity value and time, t at collision and use it to prove that the collision will occur?

 

[Chestermiller]

Homework Statement

You throw a baseball at a 45 degrees angle to the horizontal, aiming at a friend who's sitting in a tree a distance, h, above ground. At the instant you throw your ball, your friend drops another ball.

a) Show that the two balls will collide, no matter what your ball's initial speed, provided it's greater than some minimum value.
b) Find an expression for that minimum speed.

The Attempt at a Solution

Am I expected to provided an arbitrary initial velocity value and time, t at collision and use it to prove that the collision will occur?

You throw the ball by aiming it directly at your friend, as if gravity is not going to change its trajectory. If he is sitting a distance h above the ground, how far away from you horizontally is he (in terms of h)? If the initial velocity of your ball is v₀, can you determine the trajectory of your ball (x and y as functions of time). If he drops his ball with an initial velocity of zero, can you calculate the x and y locations of his ball as functions of time? Can you determine if the two trajectories meet at any time?

Chet

 

[negation]

Solved for part(a)

 

[negation]

You throw the ball by aiming it directly at your friend, as if gravity is not going to change its trajectory. If he is sitting a distance h above the ground, how far away from you horizontally is he (in terms of h)? If the initial velocity of your ball is v₀, can you determine the trajectory of your ball (x and y as functions of time). If he drops his ball with an initial velocity of zero, can you calculate the x and y locations of his ball as functions of time? Can you determine if the two trajectories meet at any time?

Chet

I have solved for part(a)
https://www.physicsforums.com/attachments/65945


How should I approach part (b)?

 

[Chestermiller]

Solved for part(a)

For part b, you just have to make sure that the collision occurs above ground.

 

[negation]

For part b, you just have to make sure that the collision occurs above ground.

The above is my answer for part(a)

I understand. But what is the initial premise from which I must work on?

Edit: I'll try working on the assumption that at t = x/vicos45, the position of my ball must be y >0m

 

[negation]

Part(b):

vi > SQRT(gx)