A supersonic jet flying at +145 m/s experiences uniform acceleration at the rate of +23.1 m/s2 for 20.0 s.
a. What is its final velocity?
b. The speed of sound is 331 m/s in air. What is the plane's speed in terms of the speed of sound?
a. To find the final velocity (v final), we can use the formula:
v final = v initial + a * t
where:
v initial is the initial velocity of the jet (145 m/s),
a is the acceleration of the jet (23.1 m/s²), and
t is the time interval (20.0 s).
v final = 145 m/s + 23.1 m/s² * 20.0 s
v final = 145 m/s + 462 m/s²
v final = 607 m/s
Therefore, the final velocity of the jet is 607 m/s.
b. We can compare the speed of the plane (v plane) to the speed of sound (v sound) using the formula:
v plane = m * v sound
where:
m is a dimensionless constant representing the ratio of the speed of the plane to the speed of sound.
By rearranging the formula, we can express the ratio (m) as:
m = v plane / v sound
Substituting the given values, we have:
m = 607 m/s / 331 m/s
m ≈ 1.834
Therefore, the plane's speed is approximately 1.834 times the speed of sound.
a. To find the final velocity, we can use the formula:
vf = vi + at
Where:
vf = Final velocity
vi = Initial velocity
a = Acceleration
t = Time
Given:
vi = +145 m/s
a = +23.1 m/s^2
t = 20.0 s
Substituting the values into the formula, we have:
vf = +145 m/s + (+23.1 m/s^2)(20.0 s)
vf = +145 m/s + (462 m/s)
vf = +607 m/s
Therefore, the final velocity of the supersonic jet is +607 m/s.
b. To find the plane's speed in terms of the speed of sound, we can divide the final velocity of the plane by the speed of sound:
Speed in terms of speed of sound = vf / speed of sound
Given:
vf = +607 m/s
speed of sound = 331 m/s
Substituting the values into the formula, we have:
Speed in terms of speed of sound = (+607 m/s) / (331 m/s)
Speed in terms of speed of sound ≈ 1.834
Therefore, the plane's speed in terms of the speed of sound is approximately 1.834 times the speed of sound.