You find yourself driving 35 kilometers an hour when you take your foot off the accelerator and descend 18 meters into the valley. Just as you reach the bottom, you see a policeman hiding between a speed limit sign that reads 70 kilometers per hour. Will he issue you a speeding ticket? Show evidence.
To determine whether you will receive a speeding ticket, we need to calculate your speed at the bottom of the valley and compare it to the posted speed limit.
Here's how you can calculate your speed at the bottom of the valley:
1. Convert the given speed from kilometers per hour (km/h) to meters per second (m/s). To do this, divide 35 km/h by 3.6 since there are 3.6 seconds in an hour (35 km/h ÷ 3.6 ≈ 9.72 m/s).
2. Use the kinematic equation v^2 = u^2 + 2as to find the final velocity (v) at the bottom of the valley, where:
- u is the initial velocity (9.72 m/s)
- a is the acceleration due to gravity (-9.8 m/s^2) since the car is descending
- s is the distance descended (18 meters)
Plugging in the values into the equation, we get:
v^2 = 9.72^2 + 2 * (-9.8) * 18
Solve for v^2:
v^2 = 94.53
Taking the square root of both sides, we find:
v ≈ 9.72 m/s
Now, we have your speed at the bottom of the valley. To determine whether you'll receive a speeding ticket, we need to compare it to the posted speed limit of 70 km/h.
Converting the speed limit to m/s, we have:
70 km/h ÷ 3.6 ≈ 19.44 m/s
Since your speed at the bottom of the valley is approximately 9.72 m/s, which is lower than the speed limit of 19.44 m/s, it is unlikely that the policeman will issue you a speeding ticket.
However, keep in mind that this calculation assumes a continuous descent with no additional factors or changes in speed. The actual circumstances may vary, so it's always best to drive within the speed limit and follow traffic regulations.