Question

The coefficient of friction between a truck's tires and the road is 0.75. A 1400 kg truck is moving at 100.0 km/h when a black bear jumps onto the highway 80.0 meters ahead. The driver has a reaction time of 0.55 seconds before the brakes are applied. Will he be able to avoid the accident? Justify your answer by showing calculations.

Answer 1

Answer on Question #37715, Physics, Mechanics

Question:

The coefficient of friction between a truck's tires and the road is 0.75. A $1400\mathrm{kg}$ truck is moving at $100.0\mathrm{km/h}$ when a black bear jumps onto the highway 80.0 meters ahead. The driver has a reaction time of 0.55 seconds before the brakes are applied. Will he be able to avoid the accident? Justify your answer by showing calculations.

Answer:

Distance before stopping will be

$$s = s _ {r} + s _ {b}$$

where $s_r$ - distance during reaction time, $s_b$ - distance after brakes are applied

$$s _ {r} = v t _ {r}$$ $$s _ {b} = \frac {v ^ {2}}{2 a}$$

Newton's laws of motion:

$$x: \quad m a = F _ {f r}$$ $$y: \quad N = m g$$

Friction force equals $F_{fr} = \mu N = \mu mg$ , $\mu$ - coefficient of friction.

Therefore:

$$a = \frac {\mu m g}{m} = \mu g$$ $$s = v t _ {r} + \frac {v ^ {2}}{2 \mu g} = 6 7. 7 m$$

So, we have $s < 80 \, m$ , therefore driver will be able to avoid the accident.

Answer: driver will be able to avoid the accident