A 747 jetliner lands and begins to slow to a stop as it moves along the runway. If its mass is 3.42×105 kg ,its speed is 29.5 m/s,and the net braking force is 4.3*10^5 N.
What is its speed 8.33 s later?
How far has it traveled in this time?
How exactly do I do this? What procedure and equations do I need?
F = m a
-4.3 * 10^5 = 3.42 * 10^5 a
the - sign is because it is braking, not speeding up.
so
a = -4.3/3.42
then
v = Vo + a t where Vo =29.5
v = 29.5 - a * 8.33
and
x = Xo + Vo t + (1/2) a t^2
distance traveled = x - Xo
= 29.5 (8.33) - (1/2)(4.3/3.42)(8.33)^2
Thanks you helped me so much!
To calculate the speed of the 747 jetliner 8.33 seconds later, as well as the distance it has traveled in that time, we need to use several equations of motion. The key equation we will use is:
v = u + at
where:
- v is the final velocity (speed) of the object,
- u is the initial velocity (speed) of the object,
- a is the acceleration,
- t is the time taken.
Let's break down the problem into steps:
Step 1: Use the given information
Given:
- Initial velocity (speed), u = 29.5 m/s
- Acceleration, a = Net braking force / mass
- Net braking force = 4.3 * 10^5 N
- Mass of the jetliner, m = 3.42 * 10^5 kg
- Time taken, t = 8.33 s
Step 2: Calculate the acceleration
To find the acceleration, we can use Newton's second law of motion: F = ma, where F is the force, m is the mass, and a is the acceleration. In this case, the net braking force is acting on the jetliner, so we can rearrange the equation to solve for acceleration:
a = F / m = (4.3 * 10^5 N) / (3.42 * 10^5 kg)
Step 3: Calculate the final velocity (speed)
Now that we have the acceleration, we can use the equation v = u + at to find the final velocity of the jetliner after 8.33 seconds.
v = u + at = (29.5 m/s) + (acceleration * 8.33 s)
Step 4: Calculate the distance traveled
To find the distance traveled, we can use another equation of motion:
s = ut + 0.5 * a * t^2
where s is the distance traveled. Rearranging the equation, we get:
s = (u * t) + (0.5 * a * t^2)
Now we can substitute the values of u, t, and a to find the distance.
s = (29.5 m/s * 8.33 s) + (0.5 * acceleration * (8.33 s)^2)
Step 5: Calculate the final results
Using the above equations, calculate both the final velocity and distance traveled:
- The speed 8.33 seconds later is the value of v obtained from step 3.
- The distance traveled is the value of s obtained from step 4.
Plug in the values and solve the equations to get the final results.
By following these steps and using the given information, you should be able to calculate the speed of the jetliner 8.33 seconds later and the distance it has traveled in that time.