Answer :
Since it isn't specified, I have to assume that when he's walking inside, along
the diagonal of the car, at 5m/s, that speed is relative to the floor of the car.
The reason I have to assume that is because I think it makes the problem
easier. I could be wrong. And it's still troubling, because 5 m/s is a hefty
11.18 mph, which is a pretty energetic walk. (In fact, it's a 5min 22sec mile,
which I for one never accomplished, even when I was running.) But so be it.
-- The length of the car's diagonal is √(3² + 15²) = √(9 + 225) = √334
-- The angle of his walk along the diagonal is the angle whose tangent is 3/15.
-- His velocity consists of the components [ 5 cos(angle) east ] and
[ 5 sin(angle) north ].
That's [ 5 x 15/√334 east ] and [ 5 x 3/√334 ] north .
The train's motion adds to the easterly component of his velocity,
and that becomes [ (2.5) + (5 x 15/√334) ] . The train's motion has
no effect on the northerly component of his velocity.
So now we're ready to put the components together and find his velocity
relative to the tracks. I think it'll be easier to go ahead and get the numerical
value of each component, and then combine them.
Easterly component: (2.5) + (5 x 15/√334) = 6.6038 m/s
Northerly component: 5 x 3/√334 = 0.8208 m/s
Just before finding the magnitude, we note that the direction of his velocity
is (the angle whose tangent is 0.8208/6.6038) north of east. That's about
7.085 degrees north of east ...the compass bearing of 82.92 degrees.
Now for the magnitude. It's the square root of the sum of the squares of
the easterly component and the northerly component.
√ (6.6038² + 0.8208²) = √44.2841 = 6.655 m/s
(All numbers are rounded.)
That's my story, and I'm sticking with it.
the diagonal of the car, at 5m/s, that speed is relative to the floor of the car.
The reason I have to assume that is because I think it makes the problem
easier. I could be wrong. And it's still troubling, because 5 m/s is a hefty
11.18 mph, which is a pretty energetic walk. (In fact, it's a 5min 22sec mile,
which I for one never accomplished, even when I was running.) But so be it.
-- The length of the car's diagonal is √(3² + 15²) = √(9 + 225) = √334
-- The angle of his walk along the diagonal is the angle whose tangent is 3/15.
-- His velocity consists of the components [ 5 cos(angle) east ] and
[ 5 sin(angle) north ].
That's [ 5 x 15/√334 east ] and [ 5 x 3/√334 ] north .
The train's motion adds to the easterly component of his velocity,
and that becomes [ (2.5) + (5 x 15/√334) ] . The train's motion has
no effect on the northerly component of his velocity.
So now we're ready to put the components together and find his velocity
relative to the tracks. I think it'll be easier to go ahead and get the numerical
value of each component, and then combine them.
Easterly component: (2.5) + (5 x 15/√334) = 6.6038 m/s
Northerly component: 5 x 3/√334 = 0.8208 m/s
Just before finding the magnitude, we note that the direction of his velocity
is (the angle whose tangent is 0.8208/6.6038) north of east. That's about
7.085 degrees north of east ...the compass bearing of 82.92 degrees.
Now for the magnitude. It's the square root of the sum of the squares of
the easterly component and the northerly component.
√ (6.6038² + 0.8208²) = √44.2841 = 6.655 m/s
(All numbers are rounded.)
That's my story, and I'm sticking with it.
