Posted by Jamie on Saturday, October 10, 2009 at 8:13pm.
An inquisitive physics student and mountain climber climbs a 50.0 m cliff that overhangs a calm pool of water. He throws two stones vertically downward, 1.00 s apart, and observes that they cause a single splash. The first stone has an initial speed of 2.08 m/s downward.
(a) How long after release of the first stone do the two stones hit the water?
(b) What initial velocity must the second stone have if they are to hit simultaneously?
2 m/s (downward)
(c) What is the speed of each stone at the instant the two hit the water?
first stone? (downward)
the second stone? (downward)

physics  MathMate, Saturday, October 10, 2009 at 9:37pm
I'd say they would never hit the water at the same time because the first stone had a initial DOWNWARD velocity of 2.08 m/s. The second stone lost one second plus it started at zero vertical velocity.
If the situation is reversed, if the second stone is given an initial downward velocity of 2.08 m/s, there is a chance they may hit the water together.
(1)
Using
S=vertical distance travelled, m
t = time in seconds since release of first stone.
S = 0*t+(1/2)(g)t² = 2.08*(t1)+(1/2)(g)(t1)²
Solve for t
(2)
v(first) = 0+(g)*t
v(second) = 2.08+(g)*(t1)
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