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?
To find the time needed for the plane to clear the intersection, we can use the equation of motion:
\[ v_f = v_i + at \]
Where:
- \( v_f \) is the final velocity of the plane (38.3 m/s)
- \( v_i \) is the initial velocity of the plane (which we assume to be 0)
- \( a \) is the deceleration of the plane (-5.33 m/s²)
- \( t \) is the time needed for the plane to clear the intersection (what we're trying to find)
We can rearrange the equation to solve for \( t \):
\[ t = \frac{{v_f - v_i}}{{a}} \]
Substituting the given values:
\[ t = \frac{{38.3 \, \text{m/s} - 0 \, \text{m/s}}}{{-5.33 \, \text{m/s}^2}} \]
Simplifying, we get:
\[ t = -\frac{{38.3}}{{5.33}} \, \text{s} \approx -7.19 \, \text{s} \]
Since time cannot be negative, we can conclude that the plane cleared the intersection in approximately 7.19 seconds.