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## Homework Statement

A freight train is moving at a constant speed of 10 m/s. A man standing on a flatcar throws a ball into the air and catches it as it falls. Relative to the flatcar, the initial vellocity of the ball is 15 m/s straight up.

a. What are the magnitude and direction of the initial velocity of the ball as seen by a second man standing on the ground next to the track?

b. How much time is the ball in the air according to the man on the train? According to the man on the ground? Mathematical prove your two answers.

c. What horizontal distance has the ball traveleed by the time it is caught according to the man on the train? According to the man on the ground?

d. What is the minimum speed of the ball during its flight according to the man on the train? According to the man on the ground?

e. What is the acceleration of the ball according to the man on the train? According to the man on the ground?

## Homework Equations

Flatcar = Train I think?

C=Car

B=Ball

G=Ground(the second man)

r[B,G] = r[B,C] + r[C,G]

## The Attempt at a Solution

r[B,C] = 0 i' + (Vi,y[B,C] *t -0.5g*t^2) j'

r[C,G] = (Vi,x[C,G] *t) i' + 0 j'

for v equations just dr/dt it.

Thus,

r[B,G] = 0 i' + (Vi,y[B,C] *t -0.5g*t^2) j' + (Vi,x[C,G] *t) i' + 0 j'

= (Vi,x[C,G] *t) i' + (Vi,y[B,C] *t -0.5g*t^2) j'

I'm just putting my answer for a) here so maybe if you guys want to verify if my solution is accurate.

V[B,G] = V[B,C] + V[C,G]

= (Vi,x[C,G]) i' + (Vi,y[B,C] -gt) j'

= (10) i' + (15-10t) j'

Since it asked for initial velocity, t=0 I guess?

= 10i' + 15j'

I'm just going straight to the point. For b),

Now as to my understanding, the ball is on air as long as r>0. Thus solving for r=0 for r[B,C], I arrived at t=3s. Now my problem is r[B,G]. I'm pretty sure t=3s as well for it, but problem is solving it mathematically as the question wanted. All I did was stated since ball is in the air only when j' > 0, then I ignored(deleted) the i' component from the equation of r[B,G], then solving it at arrive at t=3s. I wonder if there is any other way to solve it?

Oh, and btw, for e), I got dV[B,C]/dt = a[B,C] = -g j' and dV[B,G]/dt=a[B,G] = -g j'. I think that's the answer right because I remember that acceleration is the same to all observers.

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