# physics and math

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hi guys, i had the following question but i keep on getting it wrong, should i use -9.8 or 9.8 m/s2 for the acceleration? im confused and would really appreciate some help.

A student throws a set of keys vertically upward to her sorority sister, who is in a window 3.70 m above. The keys are caught 1.60 s later by the sister's outstretched hand.
(a) With what initial velocity were the keys thrown?
m/s upward

(b) What was the velocity of the keys just before they were caught?
m/s is it upwards or downwards?

thanks to anyone who can help me

• physics and math -

the sign mean direction. Gravity is downward, so if you have + as the upward direction, then gravity is downward and negative.

vf^2=vi^2+ 2acceleration*height
when the keys are caught, one wants vf to be zero.
0=vi^2+ 2 (-9.8)(+3.70)
not the plus signs upward on the height, but negative for gravity.
Solve for vi.

Just before they were caught? They were at the top, going up, near zero.

• physics and math -

g = -9.8 m/s^2 if the positive direction fot the vertical axis is defined as up.
g = +9.8 m/s^2 if the positive direction fot the vertical axis is defined as down.
You can do it either way.

(a) Assume that the keys are caught while moving up. If Y is measured upwards from the lower sister's hand,
Y = V*1.6 - (1/2) g *(1.6)^2 = 3.7 m
1.6 V = 3.7 + 12.5
Solve for V, the initial velocity.
V = +10.1 m/s

(b) When caught, v = V - gt
v = -5.6 m/s
The keys are headed back down when caught.

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