Question

A jet plane is cruising at 300 m/s when suddenly the pilot turns the engines up to full throttle. After traveling 4.9 km , the jet is moving with a speed of 400 m/s.
a. What is the jet's acceleration, assuming it to be a constant acceleration?
b-Is your answer reasonable ? Explain.

Answer 1

Answer:

a)$7.1\frac{m}{s^{2}}$

b) Yes

Explanation:

a) For an object with constant acceleration we should use the Galileo kinematic equation:

$v^{2}=v_{0}^{2}+2a\varDelta x$ (1)

with v the final velocity vo the initial velocity, a the acceleration and $\varDelta x$ the displacement to change velocity from vo to v at constant acceleration. Solving (1) for a:

$a=\frac{v^{2}-v_{0}^{2}}{2\varDelta x}=\frac{400^{2}-300^{2}}{2(4900)}$

$a=7.1\frac{m}{s^{2}}$

That acceleration is lower than acceleration of gravity g= 9.8$\frac{m}{s^{2}}$ and a jet plan is made to support accelerations higher than g and a profesional pilot trained to support it, so 7.1\frac{m}{s^{2}} is a reasonable acceleration for a jet plane.

Answer 2

Answer:

a. 7.14 m/s2

b reasonable

Explanation:

We can use the following equation of motion to find out the distance traveled by the jet:

$v^2 - v_0^2 = 2a\Delta s$

where v = 400 m/s is the final velocity of the jet, $v_0$ = 300m/s is the initial velocity of the jet, a = acceleration of the jet, which we are looking for, and $\Delta s$ = 4.9km = 4900 m is the distance traveled:

$400^2 - 300^2 = 2a4900$

$160000 - 90000 = 9800a$

$9800a = 70000$

$a = 70000 / 9800 = 7.14 m/s^2$

b. This answer is reasonable, as the jet rate increases from 300m/s to 400m/s within 4900 m distance. So it requires a fast rate of 7.14 m/s2