A jet lands at 60.2 m/s, the pilot applying the brakes 2.28 s after landing. Find the acceleration needed to stop the jet within 5.83 102 m after touchdown.
Acceleration answered in (m/s2)
If it takes t seconds to stop after braking, then
60.2 + at = 0
t = -60.2/a
Now, using the distance,
60.2*2.28 - 60.2t + 1/2 a t^2 = 583
60.2*2.28 - 60.2^2/a + 1/2 * 60.2^2/a = 583
a = -4.06 m/s^2
Well, if I were the jet, I would probably be thinking "Stop, collaborate, and listen!" But let's get to the point.
To find the acceleration needed to stop the jet, we can use the equation of motion:
v^2 = u^2 + 2as
Where:
- v is the final velocity, which is 0 m/s since the jet needs to stop
- u is the initial velocity, which is 60.2 m/s
- a is the acceleration we're trying to find
- s is the distance traveled, which is 5.83 * 10^2 m
Plugging in the values, we get:
0^2 = 60.2^2 + 2a(5.83 * 10^2)
Simplifying, we have:
0 = 3636.04 + 1166.6a
Now, let's isolate the acceleration:
1166.6a = -3636.04
Dividing both sides by 1166.6, we get:
a ≈ -3.12 m/s²
So, the acceleration needed to stop the jet within 5.83 * 10^2 m is approximately -3.12 m/s². Negative value here means that the acceleration is directed opposite to the initial velocity of the jet.
Remember, safety first, so be careful if you're ever driving a jet!
To find the acceleration needed to stop the jet within 5.83*10^2 m, we can use the equation of motion:
vf^2 = vi^2 + 2ad
Where:
- vf is the final velocity (0 m/s since the jet is stopping)
- vi is the initial velocity (60.2 m/s)
- a is the acceleration we need to find
- d is the distance traveled (5.83*10^2 m)
Rearranging the equation, we can solve for acceleration:
a = (vf^2 - vi^2) / (2d)
Plugging in the known values:
a = (0 - (60.2)^2) / (2 * 5.83*10^2)
a = (-3624.04) / (1166)
a ≈ -3.11 m/s^2
Note: The negative sign indicates that the acceleration is in the opposite direction of motion, meaning it is a deceleration or braking force.
To find the acceleration needed to stop the jet within 5.83 * 10^2 m after touchdown, we can use the equation of motion:
v^2 = u^2 + 2aS
where:
v = final velocity (0 m/s, as we want the jet to stop)
u = initial velocity (60.2 m/s, the landing speed of the jet)
a = acceleration (unknown)
S = distance traveled (5.83 * 10^2 m)
Rearranging the equation, we get:
a = (v^2 - u^2) / (2S)
Substituting the given values, we have:
a = (0^2 - 60.2^2) / (2 * 5.83 * 10^2)
Calculating this expression will give the result in (m/s^2):
a = (-3624.04) / (1166)
a ≈ -3.11 m/s^2
Note: The negative sign in the answer indicates that the acceleration is in the opposite direction of motion, which means it opposes the forward motion of the jet.