A jet plane has a takeoff speed of
vto = 74 m/s
and can move along the runway at an average acceleration of 1.6 m/s2. If the length of the runway is 2.3 km, will the plane be able to use this runway safely?
To determine if the plane will be able to use this runway safely, we need to find out if it can reach its takeoff speed within the given runway length.
First, let's convert the length of the runway from kilometers to meters:
Length of runway = 2.3 km * 1000 m/km = 2300 m
Next, we can use the kinematic equation:
v^2 = v0^2 + 2aΔx,
where:
v = final velocity (takeoff speed) = 74 m/s (given)
v0 = initial velocity (0 m/s, because the plane starts from rest)
a = acceleration = 1.6 m/s^2 (given)
Δx = displacement (length of the runway) = 2300 m (given)
Plugging in the values:
74^2 = 0^2 + 2 * 1.6 * 2300
Now, let's solve for 74^2:
5476 = 0 + 2 * 1.6 * 2300
Simplifying the equation:
5476 = 2 * 1.6 * 2300
Now, let's simplify further:
5476 = 2 * 1.6 * 2300
5476 = 2 * 3680
Finally, let's calculate the right side of the equation:
5476 = 7360
Since the equation is not balanced, it means that the plane will not be able to reach its takeoff speed of 74 m/s within the given runway length of 2300 m. Therefore, the plane will not be able to use this runway safely.