Which wave interaction is responsible for echoes?
2 answers:
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Answer:
The kangaroo was 1.164s in the air before returning to Earth
Explanation:
For this we are going to use the equation of distance for an uniformly accelerated movement, that is:
Where:
x = Final distance
xo = Initial point
Vo = Initial velocity
a = Acceleration
t = time
We have the following values:
x = 1.66m
xo = 0m (the kangaroo starts from the floor)
Vo = 0 m/s (each jump starts from the floor and from a resting position)
a = 9.8 m/s^2 (the acceleration is the one generated by the gravity of earth)
t =This is just the time it takes to the kangaoo reach the 1.66m, we don't know the value.
Now replace the values in the equation
It takes to the kangaroo 0.582s to go up and the same time to go down then the total time it is in the air before returning to earth is
t = 0.582s + 0.582s
t = 1.164s
The kangaroo was 1.164s in the air before returning to Earth
To convert parametric to Cartesian systems, you need to find a way to get rid of the t's.
In this case, the t's are inside trigonometric functions, so we're going to use a very famous trig identity you should memorize:
If we plug sin(t) and cos(t) into that equation only x and y variables will be left!
BUT there's one thing. The given cos(t + pi/6) has nasty extra stuff in it. However, part a gives you a tip on how to relate x and y to a nice clean cos(t)
So if we do a little rearranging:
Now we can plug these into the famous trig identity!
Do a little bit of adjustments to get that final form asked for, and you'll be able to find those integers of a and b. ;)
In this case, the t's are inside trigonometric functions, so we're going to use a very famous trig identity you should memorize:
If we plug sin(t) and cos(t) into that equation only x and y variables will be left!
BUT there's one thing. The given cos(t + pi/6) has nasty extra stuff in it. However, part a gives you a tip on how to relate x and y to a nice clean cos(t)
So if we do a little rearranging:
Now we can plug these into the famous trig identity!
Do a little bit of adjustments to get that final form asked for, and you'll be able to find those integers of a and b. ;)