Ancient Greek philosophers spent lots of time thinking about science and imaging explanations for the natural world. What part o
1 answer:
You might be interested in
a) Time of flight: 22.6 s
To calculate the time it takes for the cargo to reach the ground, we just consider the vertical motion of the cargo.
The vertical position at time t is given by
where
h = 2.5 km = 2500 m is the initial height
is the initial vertical velocity of the cargo
g = 9.8 m/s^2 is the acceleration of gravity
The cargo reaches the ground when
So substituting it into the equation and solving for t, we find the time of flight of the cargo:
b) 7.5 km
The range travelled by the cargo can be calculated by considering its horizontal motion only. In fact, the horizontal motion is a uniform motion, with constant velocity equal to the initial velocity of the jet:
So the horizontal distance travelled is
And if we substitute the time of flight,
t = 22.6 s
We find the range of the cargo:
To solve this problem we will apply the concepts related to the Doppler effect. The Doppler effect is the change in the perceived frequency of any wave movement when the emitter, or focus of waves, and the receiver, or observer, move relative to each other. Mathematically it can be described as,
Here,
= Frequency of Source
= Speed of sound
f = Frequency heard before slowing down
f' = Frequency heard after slowing down
v = Speed of the train before slowing down
So if the speed of the train after slowing down will be v/2, we can do a system equation of 2x2 at the two moments, then,
The first equation is,
Now the second expression will be,
Dividing the two expression we have,
Solving for v, we have,
Therefore the speed of the train before and after slowing down is 22.12m/s