A 747 jetliner lands and begins to slow to a stop as it moves along the runway. If its mass is 3.42×105 , its speed is 28.0 , and the net braking force is , what is its speed 8.27 later?
To determine the speed of the 747 jetliner 8.27 seconds later, we can use the equation:
\(v_f = v_i + at\),
where:
\(v_f\) is the final velocity,
\(v_i\) is the initial velocity,
\(a\) is the acceleration,
and \(t\) is the time.
In this case, the jetliner is slowing down, so the acceleration will be negative. The net braking force is not provided, so we cannot calculate the acceleration directly. However, we can use another equation that relates force, mass, and acceleration:
\(F = ma\),
where:
\(F\) is the net braking force,
\(m\) is the mass of the jetliner,
and \(a\) is the acceleration.
We need to rearrange this equation to solve for the acceleration \(a\):
\(a = \frac{F}{m}\).
Now, we have all the necessary information to calculate the acceleration. Let's calculate it first:
\(a = \frac{F}{m} = \frac{F}{3.42 \times 10^5 \, \text{kg}}\).
Unfortunately, the net braking force is not provided, so we cannot calculate the acceleration or the subsequent velocity.
To solve this problem, we can use the concept of acceleration and apply Newton's second law of motion. Newton's second law states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.
First, let's calculate the acceleration of the jetliner. We know that the net force acting on the jetliner is responsible for its deceleration, so we can use the formula:
Force = mass * acceleration
Rearranging the formula, we get:
Acceleration = Force / mass
Given the net braking force, we can calculate the acceleration.
Next, we'll use the formula for uniform acceleration to find the final speed of the jetliner after a given time:
v = u + at
Where:
- v is the final velocity (what we need to find)
- u is the initial velocity (given as 28.0 m/s)
- t is the time interval (given as 8.27 seconds)
- a is the acceleration (calculated in the previous step)
Let's go through the calculations step by step:
1. Calculate the acceleration:
Acceleration = Force / mass
2. Use the formula for uniform acceleration:
v = u + at
Substitute the values:
v = 28.0 m/s + (acceleration from step 1) * 8.27 seconds
Solve for v to find the final speed of the jetliner after 8.27 seconds.