Solving a Simple Free Fall Problem - Time, Velocity, and Distance Calculations

[Stumped89]

Homework Statement

Two students are on a balcony 23.5 m above the street. One student throws a ball, b1, vertically downward at 14.1 m/s. At the same instant, the other student throws a ball, b2, vertically upward at the same speed. The second ball just misses the balcony on the way down.

(a) What is the difference in time the balls spend in the air?


(b) What is the velocity of each ball as it strikes the ground?

(c) How far apart are the balls 0.520 s after they are thrown?

Homework Equations

d=vt
d=.5(v0+vf)t
d=v0t+ .5at^2

The Attempt at a Solution

I found the time it took for the first ball to hit the ground using the first formula
vt=d
14.1t=23.5
t=1.7 seconds

Next, I tried to find the time it took the second ball to hit the ground using the third equation
d=v0t+ 5at^2
47=14.1t+(4.9)t^2
I am stuck here.. I just need some guidance on how to find the time it took the second ball to hit the ground and I can figure everything else out from there, hopefully. Thanks!

 

[w3390]

First of all, the equation you used to find the time it takes for the first ball to hit the ground is missing a part. You said that the displacement is equal to the velocity times the time. However, since you are dealing with the y component you must take acceleration into account. This is done through the equation, x=v*t+(1/2)a*t^2. The key to doing part b is fully understanding what displacement means. When using the formula mentioned before, the x is displacement, not total distance. Try using this hint to figure out b.

 

[Stumped89]

Ok I've figured the velocity of the first ball to be -25.7 m/s as it strikes the ground and i understand that the total displacement for each ball as it hits the ground is -23.5 m but I still cannot quite figure out the velocity of the second ball as it hits the ground..

 

[Stumped89]

Nevermind, lol i missed it the velocity of both balls as they hit the ground are the same... thanks for the help tho!