Velo Road
car, at 35km/hr, goes down a 15m slope, at bottom = cop, will you get ticket if speed limit is 70km/hr?
So here's the full quetsion:
"You're driving at 35km/hr when the road suddenly descends 15m into a valley. You take your foot off the accelerator and coast down the hill. Just as you reach the bottom you see the policeman hiding behind the speed limit sign that reads 70km/hr. Are you going to get a speeding ticket?"
My problem is there is no angle,
I worked out that at constant velo of 35km/hr for 15m, would travel for 1.543 seconds, therefore in a down direction, acc - 9.8ms-1, therefore would increase downward direction to 0.01512km/hr, still at a constant horiz velo of 35km/hr.
but how do i know whether total speed is less than 70km/hr, seems like it would be, 15 m isnt very far... but have i got this totally wrong? thanks heaps
The question could mean that the car descends a vertical distance of 15m into the valley. If so an energy change calculation could be done using;
Ep = mgh
Work done = 0.5mv^2 - 0.5mu^2
therefore
35km/hr = 9.7222 m/s
loss of potential energy = gain in kinetic energy
mgh = 0.5mv^2 - 0.5mu^2
m's cancel
gh = 0.5v^2 - 0.5u^2
9.81 X 15 + 0.5 X 9.7222^2 = 0.5v^2
147.15 + 47.26 = 0.5v^2
194.41 X 2 = v^2
v = sqroot(388.82) = 19.71m/s
v = 70.9866 = 71 km/hr
therefore gets ticket
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