Question

Calculate the constant acceleration a in g’s which the catapult of an aircraft carrier must provide to produce a launch velocity of 188 mi/hr in a distance of 299 ft. Assume that the carrier is at anchor.

Answer 1

To calculate the constant acceleration in g's, convert the given launch velocity from mi/hr to ft/s and the given distance from ft to m. Use the kinematic equation to solve for the acceleration. The final answer will be in ft²/s² divided by m.

Step-by-step explanation:

To calculate the constant acceleration in g’s, we need to convert the given launch velocity from mi/hr to ft/s. Since 1 mi/hr is equivalent to 1.47 ft/s, the launch velocity is 188 mi/hr * 1.47 ft/s = 276.36 ft/s. We also need to convert the given distance from ft to m. Since 1 ft is equivalent to 0.3048 m, the distance is 299 ft * 0.3048 m/ft = 91.1352 m.

Now, we can use the kinematic equation:

vf² = vi² + 2ad

Where vf is the final velocity (launch velocity), vi is the initial velocity (0 since the carrier is at anchor), a is the acceleration, and d is the distance. Substituting the known values:

(276.36 ft/s)² = (0)² + 2(a)(91.1352 m)

(91.1352 m)(a) = (276.36 ft/s)²

a = [(276.36 ft/s)²] / (91.1352 m)

a = 839.7632 ft²/s² / 91.1352 m

Answer 2

The solution to the problem is as follows:

First, I'd convert 188 mi/hr to ft/s. You should end up with about ~275.7 ft/s.

So now write down all the values you know:

Vfinal = 275.7 ft/s

Vinitial = 0 ft/s

distance = 299ft

Now just plug in Vf, Vi and d to solve

Vf^2 = Vi^2 + 2 a d

BTW: That will give you the acceleration in ft/s^2. You can convert that to "g"s by dividing it by 32 since 1 g is 32 ft/s^2.