How Do You Time a Projectile to Hit a Moving Train?

[crystaluc12]

Hi, I am a newbie in this forum, and I suck at physics, please help. :) Thank you

Homework Statement

You are standing on top floor anywhere (you choose) along a measuring tape (between the pts) that runs from point A to point B. There is a train on the ground level directly below that floor. The distance between the top floor and the level of the train is h=4.95 m. Train is going from Photogate A (a sensor that beeps when train goes through) (its directly below point A) to Photogate B (directly below point B). The train is running at a constant speed along the track and parallel to the balcony. Objective is to hit the train with a "bomb" blindly. "Bomb" will be thrown from balcony. You are given a stopwatch.

1. Calculate the time it takes your bomb to drop to the level of the train
2. Calculate time it takes the train to move form the first Photogate timer to directly below you.
3. What measurements will you need to make, estimate accuracy with which measurements need to be made, and how will you determine when to drop your projectile.

acceleration (a)=-g=-9.8 m/s^2

Homework Equations

I think:
x=(1/2)a*t^2+v(sub 0)+x (sub 0)
x=v(sub 0)*t+x(sub 0)

The Attempt at a Solution

1. For this one I thought that the initial velocity v(sub 0) would be equal to 0 since I would be dropping it from the top without any starting velocity. The initial height would be equal to 4.95 and acceleration is -9.8. So I did:

x=(1/2)a*t^2+v(sub 0)+x (sub 0)
0=(1/2)(-9.8)*t^2+0+4.95
-4.95=-4.9*t^2
t=square root (1.011)=approx 1

I am not sure if my calculations are correct.

2. I thought that it was calculated using x=v(sub 0)*t+x(sub 0)
so I thought that initial velocity of the train moving from a to b would be zero. So I put:
t=-x (sub 0)/v(sub 0)
But since v(sub 0) =0 the formula does not seem right to me. What formula do I need to use?

3. I thought that some measurements would be: I just drop my "bomb" many times from different measurements along the measuring tape and timed how long it took the "bomb" to drop and a) hit the train, b) miss the train, c) nearly hit the train. I need to know how long the train needs to get from 1st photogate to directly below me. I thought that listening for the beeps of the photogate and for sound of train and dropping it by a guess of when I thought the train was nearby would help me determine when to drop the "bomb"

I really am not sure if this is correct or if I am going at it the right way.

 

[Astronuc]

The problem states that the 'bomb' will be thrown, so the bomb will have any initial velocity. Also one can stand 'anywhere' do distance from point A is a variable, and one does not know the velocity of the train.

I think the problem is one of establish the distance from point A and velocity of the train as variables and relating them to the initial velocity of the bomb.

The equations:
x=(1/2)a*t^2+v(sub 0)+x (sub 0)
x=v(sub 0)*t+x(sub 0)

are correct keeping in mind that x is vertical position.

Ostensibly, one decides distance from A. Then how to determine the velocity of the train. Well knowing the length of the train, L, and the time it takes to pass gate A would give a speed. Then there is the time it takes to get to one's position, and there is the time interval the train spends passing one.