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 intersection is 21.3 m. The plane decelerates through the intersection at a rate of 5.33 m/s2 and clears it with a final speed of 38.3 m/s. How much time is needed for the plane to clear the intersection?
7.65 s
To find the time needed for the plane to clear the intersection, you can use the equation of motion:
v_f = v_i + at
Where:
v_f = final velocity (38.3 m/s)
v_i = initial velocity (unknown, assumed to be zero)
a = acceleration (-5.33 m/s^2)
t = time (unknown)
First, let's find the initial velocity (v_i). Since the plane is decelerating, we can assume that the initial velocity is zero.
Now, rearrange the equation to solve for time (t):
t = (v_f - v_i) / a
Since v_i is zero, the equation simplifies to:
t = v_f / a
Substitute the given values into the equation:
t = 38.3 m/s / -5.33 m/s^2
Now, calculate the time:
t = -7.19 s
However, time cannot be negative in this case because it represents the duration. Therefore, we can take the absolute value of the time:
t = | -7.19 s |
So, the time needed for the plane to clear the intersection is approximately 7.19 seconds.