A ball is thrown directly downward with an initial speed of 7.65 m/s froma height of 29.0 m. After what time interval does it st
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Average force on the window: 0.32 N
Explanation:
The average force exerted on the window is given by Newton's second law
where
is the net change in momentum of the hailstones in a time interval of
In order to find the change in momentum, we have to consider only the component of the hailstone's momentum perpendicular to the window, therefore:
is the initial momentum of one hailstone, with
m = 7 g = 0.007 kg is the mass
is the initial speed
is the angle with the window
The final momentum is
where
v = 4.5 m/s is the final speed (the collision is elastic so the speed is equal, while the direction changes)
(after the rebound, the direction has changed)
So the change in momentum of 1 hailstone is
We are interested only in the magnitude, so
There are 595 hailstones hitting the window in 49 s, so the total change in momentum is
And therefore, the average force on the window is
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To develop this problem it is necessary to apply the concepts related to the Dopler effect.
The equation is defined by
Where
= Approaching velocities
= Receding velocities
c = Speed of sound
v = Emitter speed
And
Therefore using the values given we can find the velocity through,
Assuming the ratio above, we can use any f_h and f_i with the ratio 2.4 to 1
Therefore the cars goes to 145.3m/s