# Projected motion/trajectory question [EASY]

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1. Jan 31, 2017

### ujellytek

1. The problem statement, all variables and given/known data
The rock 'A' is dropped 100m above a river. After 2 seconds, rock 'B' is thrown down from the same height. What initial velocity must be given to rock 'B' so that both rocks hit the river at the exact same time? [No air resistance]

2. Relevant equations

3. The attempt at a solution
http://imgur.com/a/59fkU

Rock A: v1=0 During a 2s drop it travels 19.6m, -4.9(2)^2+100
So the equation for rock A is d=-4.9(t)^2+80.4
When will rock A hit the river? isolate t and I get ~4.0507 seconds

Rock B: v1=? equation is easy to set up: d=-4.9(t)^2+v1(t)+100 (starts 19.6m behind the dropped rock)
Now we sub in the time rock A hits the river: (4.9(4.0507)^2-100) * (4.0507)^-1=v1
This gives me an answer of ~-4.849m/s

Last edited: Jan 31, 2017
2. Jan 31, 2017

### Staff: Mentor

That's relevant equations, not relevant questions. What common kinematic equations might apply to this problem?

3. Jan 31, 2017

### ujellytek

Done

4. Jan 31, 2017

### Staff: Mentor

I think you forgot the velocity that rock A had attained by the time it reached the 2 second mark when you wrote its equation. I think you'll find that the time remaining for rock A to hit the water from the 2 second point is much less than 4 seconds.

5. Jan 31, 2017

### ujellytek

You're right, thanks. The velocity then turns out to be ~27.38m/s instead of 4.849m/s

6. Jan 31, 2017

### Staff: Mentor

That certainly looks better!