A child drops a ball onto the road 28 m in front of a car travelling at 50 km/h. If the car can decelerate at a rate of 3.5 m/s2, will it stop before hitting the ball?
Vc = 50km/h = 50000m/3600s = 13.89 m/s.
d = (Vf^2-Vo^2)/2a.
d = (0-(13.89)^2) / -7 = 27.56 m.
Yes, it will stop before hitting the ball; but it will be very close!
Well, it looks like the ball has decided to play a game of chicken with the car. If the car can decelerate at a rate of 3.5 m/s², let's see if it has what it takes to win the game!
First, let's convert the car's speed to m/s because apparently, the ball is a stickler for the metric system. So, 50 km/h is equivalent to 50 * (1000/3600) m/s, which is approximately 13.9 m/s.
Now, let's calculate the time it takes for the car to reach the ball. We can use the formula: time = distance / speed. So, time = 28 m / 13.9 m/s, which is approximately 2.01 seconds.
During this time, the car will be decelerating, so we need to use a different formula to calculate the distance it will cover while decelerating. The formula is: distance = initial velocity * time + 0.5 * acceleration * time².
Plugging in the values, distance = 13.9 m/s * 2.01 s + 0.5 * (-3.5 m/s²) * (2.01 s)². After solving this equation, we find that the car will cover a distance of approximately 25.8 meters while decelerating.
Since the ball is 28 meters away, it seems like the car will just barely make it! Phew! Good thing the car is a quick thinker and a good breaker, otherwise it would have been a real smash hit!
Remember, this is all assuming perfect conditions and no delays in the car's braking system. So don't take this as an invitation to play chicken with speeding cars, okay? Safety first, everyone!
To determine if the car will stop before hitting the ball, we need to calculate the distance it would take for the car to come to a stop.
First, let's convert the car's speed from km/h to m/s:
50 km/h * (1000 m/1 km) * (1 h/3600 s) = 13.89 m/s
Using the formula for distance traveled during deceleration:
distance = (initial velocity)^2 / (2 * deceleration)
distance = (13.89 m/s)^2 / (2 * 3.5 m/s^2)
distance = 96.84 m
The car will travel a distance of 96.84 m before coming to a stop. Since the ball is 28 m in front of the car, the car will not stop in time and will hit the ball.
To determine if the car will stop before hitting the ball, we need to compare the distance the car will travel while braking to the distance between the car and the ball.
Let's calculate the distance the car will travel while braking. We know the initial velocity of the car is 50 km/h, which we need to convert to m/s:
1 km/h = 1000 m / 3600 s = 0.2778 m/s
Therefore, the initial velocity of the car is:
50 km/h * 0.2778 m/s = 13.89 m/s
Next, we need to determine the stopping distance of the car. We can use the formula:
Stopping distance = (initial velocity)^2 / (2 * deceleration)
Plugging in the values we have:
Stopping distance = (13.89 m/s)^2 / (2 * 3.5 m/s^2)
Stopping distance = 192.5 m^2/s^2 / 7 m/s^2
Stopping distance = 27.5 m
Now, we compare the stopping distance to the distance between the car and the ball. The ball is 28 m in front of the car. Since the stopping distance is less than the distance to the ball, the car will not be able to stop in time and will hit the ball.