A small propeller airplane can comfortably achieve a high enough speed to take off on a runway that is 1/4 mile long. A large, fully loaded passenger jet has about the same acceleration from rest, but it needs to achieve twice the speed to take off. What is the minimum runway length that will serve? Hint: You can solve this problem using ratios without having any additional information.

1 mile

Explanation:

We can use the following equation of motion to solve for this problem:

where v m/s is the final take-off velocity of the airplane, initial velocity of the can when it starts from rest, a is the acceleration of the airplanes, which are the same, and is the distance traveled before takeoff, which is minimum runway length:

From here we can calculate the distance ratio

Since the 2nd airplane has the same acceleration but twice the velocity

So the minimum runway length is 1 mile

initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft