Question

a jet fighter plane is launched from a catapult on an aircraft carrier. it reaches a speed of 42 m/s at the end of the catapult, and this requires 2.0 s. assuming the acceleration is constant, what is the length of the catapult? 16 m 24 m 42 m 84 m

Explanation:

Step1: Identify known quantities

The jet starts from rest (initial velocity \( u = 0 \, \text{m/s} \)), final velocity \( v = 42 \, \text{m/s} \), time \( t = 2.0 \, \text{s} \), and acceleration is constant. We can use the formula for average velocity to find the displacement (length of catapult), since for constant acceleration, average velocity \( \bar{v}=\frac{u + v}{2} \), and displacement \( s=\bar{v}\times t \).

Step2: Calculate average velocity

\( \bar{v}=\frac{0 + 42}{2}=21 \, \text{m/s} \)

Step3: Calculate displacement (length of catapult)

Using \( s=\bar{v}\times t \), substitute \( \bar{v} = 21 \, \text{m/s} \) and \( t = 2.0 \, \text{s} \):
\( s=21\times2.0 = 42 \, \text{m} \)

Answer:

42 m (corresponding to the option "42 m")