A plane traveling at 200.0 km/h attempts to land on a 250 m runway. The plane’s engines and brakes accelerate uniformly at –7.0 m/s2. Will the plane be able to land safely? Show all your work. Include any equations used, including the given and the unknown. Show all calculations. Express numerical answers with the correct number of significant digits. Remember to carry one or two extra decimal places throughout your calculations; do not round until the end.
vf^2=vi^1+2ad
solve for d. Is it within the 250m runway?
To solve this problem, we need to determine if the plane can stop within the given runway length. We can do this by calculating the distance it takes for the plane to come to a stop using the equations of motion.
Given:
Initial velocity, u = 200.0 km/h (convert to m/s)
Acceleration, a = -7.0 m/s^2
Final velocity, v = 0 m/s
Distance, s = 250 m
To solve the problem, we can use the equation of motion that relates distance, initial velocity, final velocity, and acceleration:
v^2 = u^2 + 2as
Rearranging the equation, we can solve for acceleration:
a = (v^2 - u^2) / (2s)
Now we can substitute the given values into the equation and calculate:
1. Convert initial velocity from km/h to m/s:
u = 200.0 km/h x (1000 m/1 km) x (1 h/3600 s) ≈ 55.56 m/s
2. Substitute the values:
a = (0^2 - 55.56^2) / (2 * 250)
a = (-3086.4) / 500
a = -6.17 m/s^2
Since the calculated acceleration (-6.17 m/s^2) is less than the given acceleration (-7.0 m/s^2), the plane will be able to land safely within the given runway length.
Therefore, the plane will be able to land safely.