The distance - time graph of the humming bird is missing, so i have attached it.
Answer:
Instantaneous velocity = 0.5 m/s
Explanation:
From the attached graph, at time t = 1 s, the corresponding distance is 0.5 m.
Instantaneous velocity is the velocity at that point.
Thus;
Instantaneous velocity = 0.5/1
Instantaneous velocity = 0.5 m/s
Complete Question
A commuter train passes a passenger platform at a constant speed of 39.6 m/s. The train horn is sounded at its characteristic frequency of 350 Hz.
(a)
What overall change in frequency is detected by a person on the platform as the train moves from approaching to receding
(b) What wavelength is detected by a person on the platform as the train approaches?
Answer:
a
b
Explanation:
From the question we are told that
The speed of the train is
The frequency of the train horn is
Generally the speed of sound has a constant values of
Now according to dopplers equation when the train(source) approaches a person on the platform(observe) then the frequency on the sound observed by the observer can be mathematically represented as
substituting values
Now according to dopplers equation when the train(source) moves away from the person on the platform(observe) then the frequency on the sound observed by the observer can be mathematically represented as
substituting values
The overall change in frequency is detected by a person on the platform as the train moves from approaching to receding is mathematically evaluated as
Generally the wavelength detected by the person as the train approaches is mathematically represented as
(a) 30.9 m
Let's analyze the motion of the parachutist. Its vertical position above the ground is given by
where
h = 45 m is the initial height
u = 10 m/s is the initial velocity (upward)
t is the time
g = -9.8 m/s^2 is the acceleration of gravity (downward)
Substituting t=3 s , we find the height of the parachutist when it opens the parachute:
(b) 44.1 m
Here we have to find first the height of the balloon 3 seconds after the parachutist has jumped off from it. The vertical position of the balloon is given by
y = h + ut
where
h = 45 m is the initial height
u = 10 m/s is the initial velocity (upward)
t is the time
Substituting t = 3 s, we find
y = 45 m + (10 m/s)(3 s) = 75 m
So the distance between the balloon and the parachutist after 3 s is
d = 75 m - 30.9 m = 44.1 m
(c) 8.2 m/s downward
The velocity of the parachutist at the moment he opens the parachute is:
v = u +gt
where
u = 10 m/s is the initial velocity (upward)
t is the time
g = -9.8 m/s^2 is the acceleration of gravity (downward)
Substituting t = 3 s,
v = 10 m/s + (-9.8 m/s^2)(3 s)= -19.4 m/s
where the negative sign means it is downward
After t=3 s, the parachutist open the parachute and it starts moving with a deceleration of
a =+5 m/s^2
where we put a positive sign since this time the acceleration is upward.
The total distance he still has to cover till the ground is
d = 30.9 m
So we can find the final velocity by using
where this time we have u = 19.4 m/s as initial velocity. Taking the downward direction as positive, the deceleration must be considered as negative:
a = -5 m/s^2
Solving for v,
(d) 5.24 s
We can find the duration of the second part of the motion of the parachutist (after he has opened the parachute) by using
where
a = -5 m/s^2 is the deceleration
v = 8.2 m/s is the final velocity
u = 19.4 m/s is the initial velocity
t is the time
Solving for t, we find
And added to the 3 seconds between the instant of the jump and the moment he opens the parachute, the total time is
t = 3 s + 2.24 s = 5.24 s
Answer:
Approximately to the right (assuming that both astronauts were originally stationary.)
Explanation:
If an object of mass is moving at a velocity of
, the momentum
of that object would be
.
Since momentum of this system (of the astronauts) conserved:
.
Assuming that both astronauts were originally stationary. The total initial momentum of the two astronauts would be since the velocity of both astronauts was
.
Therefore:
.
The final momentum of the first astronaut (,
to the left) would be
to the left.
Let denote the momentum of the astronaut in question. The total final momentum of the two astronauts, combined, would be
.
.
Hence, . In other words, the final momentum of the astronaut in question is the opposite of that of the first astronaut. Since momentum is a vector quantity, the momentum of the two astronauts magnitude (
) but opposite in direction (to the right versus to the left.)
Rearrange the equation to obtain an expression for velocity in terms of momentum and mass:
.
.
Hence, the velocity of the astronaut in question () would be
to the right.