Confusing Physics Question about initial and final velocity?

Question

I'm taking honors physics this year, and I've come across a problem that I really don't understand.
Here's the question:

"A student throws a set of keys vertically upward to her sorority sister, who is in a window 4.00 m above. The keys are caught 1.50 s later by the sister's outstretched hand.
(a) With what initial velocity were the keys thrown?
(b) What was the velocity of the keys just before they were caught?"

Here is what I'm assuming from the problem:
(a) is asking initial velocity (v0)
(b) is asking final velocity (vf)
delta d is 4.00 m
delta t is 1.50 s
Average Velocity is 2 and 2/3 m/s (Because velocity = distance/time)


I can't for the life of me figure out how to find the initial and final velocities. Can someone please explin this to me?

Thanks!!!

Answer 1

Use the position formula, s(t) = (1/2)gt^2 + v(init)t + s(init).
We shall say that the initial position, s(init), is zero as we are measuring relative to the student tossing the keys.
Time, t, is 1.5 seconds.
Gravity is a constant -9.8m/s^2.
The position at 1.5 seconds is, s(1.5) = 4 m.

Substitute and solve for v(init).

4 = (1/2)(-9.8)(1.5)^2 + v(init)*(1.5) + 0
(1.5)*v(init) = 15
v(init) = 10 m/s, the initial velocity of the keys.

To get the velocity of the keys use the velocity formula, or the derivative of the position formula, v(t) = gt + v(init).
Use the same constant for gravity, the same time, and the newly discovered initial velocity so solve.

v(1.5) = (-9.8)(1.5) + 10
v(1.5) = -14.7 + 10
v(1.5) = -4.7 m/s is the velocity.
This means that the keys were falling 4.7 m/s when they were caught.

Answer 2

The 1st answer you got is right. You can solve it intuitively after calculating what the delta V would be.

delta V = g*1.5 sec. Then if your average velocity is halfway between Vo and Vf ...

Answer 3

try this formula Y=V(f)t-1/2gt
Dont forget you got gravity acting on the keys.
4m=V(f) x 1.5s-1/2 x 9.8m/s^2 x 1.5s^2
V(f)=7.5m/s
V(y)=V(f)-gt=7.5m/s+9.8m/s x 1.5s=22.2m/s