- #1
Max0007
- 66
- 1
Homework Statement
The top of a 10-storey building (42 m) , someone throws a ball (A) down with a
initial speed of 2.5 m / s. You are on the second floor (8 m window above the ground) and
You throw a ball (B) upward with an initial speed of 22 m / s.
a) If both balls are thrown together after how much time do they intersect ?
b) It is hoped that the two balls, launched with the same speed and in the same direction , strike
the soil simultaneously. Which bullets (A or B) is to be launched first? how
time before the other ball should it be launched ?
Homework Equations
Initial Speed for A: 2.5 m/s
height B initial: 42 m
height B final: 0 m
Initial Speed for B: 22 m/s
height B initial: 8 m
height B final: 0 m
The Attempt at a Solution
a)
height final= height initial + Initial speed *(final time - initial time) - g/2 *(final time - initial time)^2
0=8 + 22m/s * (time) - 9.81/2 * (time)^2
0=42 + 2.5m/s * (time) - 9.81/2 * (time)^2
To find the the time when it intersect I did this:
42 + 2.5m/s * (time) - 9.81/2 * (time)^2 = 8 + 22m/s * (time) - 9.81/2 * (time)^2
and found 1.74seconds
For b)
I found at what time they both hit the ground.
0=42 + 2.5m/s * (time) - 9.81/2 * (time)^2 // A hits the ground in 3.19 secs
0=8 + 22m/s * (time) - 9.81/2 * (time)^2 // B hits the ground in 4.82 secs
I want to trow B first because it takes longer than A to hit the ground.
Now since B hits the ground in 4.82 secs I will replace 4.82 sec in this 42 + 2.5m/s * (time final - time initial) - 9.81/2 * (time final - time initial)^2 , I will replace it in time final. So I will have to find the time initial. I want A to hit the ground the same time as B.
42 + 2.5m/s * (4.82 - time initial) - 9.81/2 * (4.82- time initial)^2=0
I find 2.14 secs.
Can you guys verify that its all good please ? I really appreciate it :)