To determine the thickness of the barriers needed to safely stop a car that hits them at a speed of 110 km/h, we first need to convert the speed from kilometers per hour to meters per second.
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Convert speed:
\[ 110 , \text{km/h} = 110 \times \frac{1000 , \text{m}}{1 , \text{km}} \times \frac{1 , \text{h}}{3600 , \text{s}} = \frac{110000 , \text{m}}{3600 , \text{s}} \approx 30.56 , \text{m/s} \] -
Using the formula for acceleration and the kinematic equation:
We'll use the equation relating final velocity, initial velocity, acceleration, and distance. The equation is:\[ v^2 = u^2 + 2a d \]
where:
- \( v = 0 , \text{m/s} \) (final velocity, as the car comes to a stop)
- \( u = 30.56 , \text{m/s} \) (initial velocity)
- \( a = -300 , \text{m/s}^2 \) (acceleration, negative because it's deceleration)
- \( d \) is the distance (thickness of the barrier) we want to find.
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Substituting values into the equation:
Rearranging the formula for \( d \):\[ 0 = (30.56)^2 + 2(-300)d \]
Rearranging gives:
\[ (30.56)^2 = 600d \]
Now we calculate \( (30.56)^2 \):
\[ (30.56)^2 \approx 933.4336 \]
Now solve for \( d \):
\[ d = \frac{933.4336}{600} \approx 1.55572 , \text{m} \]
Thus, to safely stop a car hitting the barrier at 110 km/h, the soft barrier should be approximately 1.56 meters thick.
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