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Your older brother is driving at 35 km/h when the road suddenly descends 15 m into a valley. He takes his foot off the accelerator and coasts down the hill. Just as he reaches the bottom you see a policeman hiding behind the speed limit sign that reads "70 km/h." Is your brother going to get a speeding ticket?

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Answer:

Yes

Explanation:

m = Mass of car

g = Acceleration due to gravity = 9.81 m/s²

u = Initial velocity = 35 km/h

v = Final velocity

h = Altitude = 15 m

Here, the energy is conserved

[tex]KE=PE\\\Rightarrow \frac{1}{2}m(v^2-u^2)=mgh\\\Rightarrow v=\sqrt{2gh+u^2}\\\Rightarrow v=\sqrt{2\times 9.81\times 15+\left(\frac{35}{3.6}\right)^2}\\\Rightarrow v=17.15517\ m/s[/tex]

Converting to km/h

[tex]1\ m/s=3.6\ km/h[/tex]

[tex]\\\Rightarrow 19.71855=19.71855\times 3.6\ km/h=70.98678\ km/h[/tex]

The speed of the car is 70.98678 km/h is greater than 70 km/h.

Hence, a speeding ticket will be given

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