a man is traveling at 43 km per hour , a child jumps out in front of his car 13 meters ahead , with a deceleration rate of 8 meters per second squared, and a reaction time of .5 seconds , will the man stop before hitting the child
To determine if the man will stop before hitting the child, we can calculate the distance the man will travel during his reaction time and the distance he will travel while decelerating.
First, let's calculate the distance traveled during the reaction time of 0.5 seconds. Since the man is traveling at 43 km/h, we need to convert this speed to meters per second:
Speed in meters per second = (43 km/h) * (1000 m/km) / (3600 s/h)
= (43 * 1000) / (3600)
≈ 11.94 m/s
During the reaction time, the man will cover a distance of:
Distance during reaction time = (Speed during reaction time) * (Reaction time)
= 11.94 m/s * 0.5 s
= 5.97 meters
Now, let's calculate the distance the man will travel while decelerating. The formula to calculate the deceleration distance is:
Deceleration distance = (Initial velocity)^2 / (2 * Deceleration rate)
= (Speed during reaction time)^2 / (2 * Deceleration rate)
= (11.94 m/s)^2 / (2 * 8 m/s^2)
= 143.04 meters / (2 * 8)
= 143.04 meters / 16
≈ 8.94 meters
Finally, to determine if the man will stop before hitting the child, we add the distance traveled during the reaction time to the deceleration distance:
Total distance traveled = Distance during reaction time + Deceleration distance
= 5.97 meters + 8.94 meters
≈ 14.91 meters
Since the distance the child jumped out is 13 meters, and the man will travel approximately 14.91 meters before coming to a full stop, it means the man will not stop before hitting the child.