A Boeing 747 “Jumbo Jet” has a length of 59.7 m. The runway on which the plane lands intersects another runway. The width of the inter- section is 25.0 m. The plane decelerates through the intersection at a rate of 6.1 m/s2 and clears it with a final speed of 45.0 m/s. How much time is needed for the plane to clear the intersection?
V^2 = Vo^2 + 2a*d. V = 45 m/s, a = -6.1 m/s^2, d = 59.7m+25m, Vo = ?.
V = Vo + a*t. V = 45 m/s, Vo = previous calculation, a = -6.1 m/s^2, t = ?.
To find the time needed for the plane to clear the intersection, we can use the equation of motion:
v^2 = u^2 + 2as
Where:
v = final velocity (45.0 m/s)
u = initial velocity (assumed to be 0 m/s, since the problem does not provide it)
a = acceleration (-6.1 m/s^2, deceleration is considered negative)
s = displacement (total distance the plane needs to travel to clear the intersection)
First, let's find the displacement (s) covered by the plane to clear the intersection. The total distance is the sum of the length of the plane (59.7 m) and the width of the intersection (25.0 m):
s = length of plane + width of intersection
s = 59.7 m + 25.0 m
s = 84.7 m
Now, we can plug the values into the equation of motion and solve for time (t):
v^2 = u^2 + 2as
(45.0 m/s)^2 = 0^2 + 2(-6.1 m/s^2)(84.7 m)
2025 m^2/s^2 = -12.2 m/s^2 * 169.4 m
2025 m^2/s^2 = -2064.28 m^2/s^2
As we can see, the equation does not make sense. This means the plane cannot clear the intersection with the given values.
It's possible that there is some missing information or mistake in the problem statement. I would recommend double-checking the given values or providing additional information to solve the problem accurately.