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My first question:

1. A baseball pitcher throws a ball vertically upward and catches it at the same level 4.2s later.

a) With what velocity did the pitcher throw the ball?

b) How high did the ball rise?

(my work, which is wrong according to the book)

a)

[itex]v_2 = v_1 + (a)\Delta(t)

= 0m/s - (-9.80m/s^2)(4.2s)

= 41m/s [up][/itex]

The book says it's 21m/s [up], but I don't really see why, so could someone please tell me what I did wrong, or if I'm actually correct, while the book is wrong(the books have been wrong several times before).

b)

I haven't started this yet, because I think I need the initial veolocity in order to calculate the displacement. Would I be correct to use this equation?

[itex]\Delta(d) = v_1\Delta(t) + 1/2a\Delta(t)^2[/itex]

Now for my second question:

There are many well-documented cases of people falling from tremendous heights without parachutes and surviving. The record is held by a Russian who fell from an astounding 7500m. The chances of survival depend on the "deceleration distance" at the time of landing. Why is a fall from a height of 7500m no motr dangerous than one from half that height? How can the deceleration distance upon landing be maxized?

I think I got the first part, because of terminal speed, there wouldn't be a difference in between the two speeds acheived from the falls(assuming the fall from half that height achieves terminal speed). But the second part has me stuck, the question doesn't really explain what the deceleration distance is, so I don't know how to maximize it, or much about it all, for that matter.

1. A baseball pitcher throws a ball vertically upward and catches it at the same level 4.2s later.

a) With what velocity did the pitcher throw the ball?

b) How high did the ball rise?

(my work, which is wrong according to the book)

a)

[itex]v_2 = v_1 + (a)\Delta(t)

= 0m/s - (-9.80m/s^2)(4.2s)

= 41m/s [up][/itex]

The book says it's 21m/s [up], but I don't really see why, so could someone please tell me what I did wrong, or if I'm actually correct, while the book is wrong(the books have been wrong several times before).

b)

I haven't started this yet, because I think I need the initial veolocity in order to calculate the displacement. Would I be correct to use this equation?

[itex]\Delta(d) = v_1\Delta(t) + 1/2a\Delta(t)^2[/itex]

Now for my second question:

There are many well-documented cases of people falling from tremendous heights without parachutes and surviving. The record is held by a Russian who fell from an astounding 7500m. The chances of survival depend on the "deceleration distance" at the time of landing. Why is a fall from a height of 7500m no motr dangerous than one from half that height? How can the deceleration distance upon landing be maxized?

I think I got the first part, because of terminal speed, there wouldn't be a difference in between the two speeds acheived from the falls(assuming the fall from half that height achieves terminal speed). But the second part has me stuck, the question doesn't really explain what the deceleration distance is, so I don't know how to maximize it, or much about it all, for that matter.

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