The takeoff runway on carriers is much too short for a modern jetplane to take off on its...

The takeoff runway on carriers is much too short for a modern jetplane to take off on its own. For this reason, the takeoff of carrier planes is assisted by hydraulic catapults (Fig. A). The catapult system is housed below the deck except for a relatively small shuttle that slides along a rail in the middle of the runway (Fig. B). The front landing gear of carrier planes is equipped with a tow bar that, at takeoff, is attached to the catapult shuttle (Fig. C). When the catapult is activated, the shuttle pulls the airplane along the runway and helps the plane reach its takeoff speed. The takeoff runway is approximately 300 ft long, and most modern carriers have three or four catapults.

Figure P5.8

If the carrier takeoff of a 45,000 lb plane subject to the 32,000 lb thrust of its engines were not assisted by a catapult, estimate how long it would take for a plane to safely take off, i.e., to reach a speed of 165 mph starting from rest. Also, how long a runway would be needed under these conditions?