step by step please A fighter jet taking off from an aircraft carrier must gain

Question

step by step please

A fighter jet taking off from an aircraft carrier must gain a relatively high speed over a relatively short distance. A fighter jet must go from a speed of zero to 112 miles/hour over a distance of 192 feet. Assuming the jet is gaining speed at constant acceleration, how many g's of acceleration does the pilot feel in the horizontal direction? (Use 1 mile = 1609 meters = 5280 feet.) 1 g = 10 m sec^2. A rocket (initially at rest) is fired vertically from the ground with a constant upward acceleration. After 20 seconds, the engines turn off and the rocket continues upward, being slowed by gravity. The total time between the rocket leaving the ground and reaching the top of its trajectory is 60 seconds. (Assume air resistance can be ignored.) What is the upward acceleration of the rocket? What is the maximum height reached by the rocker?

Explanation / Answer

4.

consider the motion of the rocket while accelerating up for 20 sec :

Vo = initial velocity

a = acceleration

Vf = final velocity after 20 sec

t = 20 sec

using the equation

Vf = Vo + at = 0 + a (20) = 20 a

D = distance travelled in first 20 sec = Vot + (0.5) at2 = 0 (20) + (0.5) a (20)2 = 200 a

consider the motion after engine turns off :

t' = time of travel = 60 - 20 = 40 sec

Vf' = velocity at the highest position = 0

a' = acceleration = - 9.8

using the equation

Vf' = Vf + a' t'

0 = 20 a + (- 9.8) (40)

a = 19.6 m/s2

D' = distance travelled after engine turns off

using the equation

D' = Vf' t' + (0.5) a' t'2

D' = (20a) (40) + (0.5) (-9.8) (40)2

D' = (20 x 19.6 ) (40) + (0.5) (-9.8) (40)2

D' = 7840 m

maximum height reached = H = D + D' = 200 a + 7840 = 200 (19.6) + 7840 = 11760 m

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