Answers:
a)The balloon is 68 m away of the radar station
b) The direction of the balloon is towards the radar station
Explanation:
We can solve this problem with the Doppler shift equation:
(1)
Where:
is the actual frequency of the sound wave
is the "observed" frequency
is the velocity of sound
is the velocity of the observer, which is stationary
is the velocity of the source, which is the balloon
Isolating :
(2)
(3)
(4) This is the velocity of the balloon, note the negative sign indicates the direction of motion of the balloon: It is moving towards the radar station.
Now that we have the velocity of the balloon (hence its speed, the positive value) and the time (
) given as data, we can find the distance:
(5)
(6)
Finally:
(8) This is the distance of the balloon from the radar station
Answer:
2) f = 0.707 Hz
Explanation:
Given m₁ = 1.0 kg , f₁ = 1.0 Hz
So using the equation
f₁ = ( 1 / 2 π ) * √K / m₁
Solve to determine K' constant of spring
K = m * ( 4 π ² * f ² )
K = 1.0 kg * ( 4 π ² 1.0² Hz )
K = 39.4784176
So given 2.0 kg the frequency can be find using formula
f₂ = ( 1 / 2 π ) * √K / m₂
f₂ = ( 1 / 2 π ) * √39.4784176 / 2.0 kg
f₂ = 0.707 Hz
We know the formulas for momentum and energy. But they both involve the mass of
the object, and we don't know the mass of the baseball. What can we do ?
It's not a catastrophe. The question only asks which one is bigger. If we're clever,
we can answer that without ever knowing how much the momentum or the energy
actually is. We know that both baseballs have the same mass, so let's just call it
' M ' and not worry about what it really is.
<u>Momentum of anything = (mass) x (speed)</u>
Momentum of the first baseball = (M) x (4 m/s) = 4M
Momentum of the second one = (M) x (16 m/s) = 16M
The second baseball has 4 times as much momentum as the first one has.
<u>Kinetic energy of anything = 1/2 (mass) x (speed squared)</u>
KE of the first baseball = 1/2 (M) x (4 squared) = 8M
KE of the second one = 1/2 (M) x (16 squared) = 128M
The second baseball has 16 times as much kinetic energy as the first one has.
Cognitive:
This is because teens tend to excrete more hormones when they are in their adolescent ages causing them to act in a riskier behavior.
Emotions:
Because of their feeling that they want to have freedom.
Physical:
Their hormones are affecting their actions.
It’s to push an object in it’s direction of where it’s leading to.
