An airplane is flying at 95.0 m/s when the engine is turned off. As it glides, it experiences a force of drag so that is slows down at -0.700 m/s2. How far in meters will it travel in 1.00 minute ?
answer: 4440m??
t = 60 seconds
Vi = 95 m/s
a = - 0.7 m/s^2
x = X1 + 95 t - 0.35 t^2
x - xi = distance = 95(60) - .35(60)^2
= 5700 - 1260
= 4440 yes
To determine the distance the airplane will travel, we can use the formula for distance traveled when decelerating uniformly. The formula is:
d = (v^2 - u^2) / (2a)
where:
d = distance traveled
v = final velocity
u = initial velocity
a = deceleration (negative value)
Given:
u = 95.0 m/s (initial velocity)
a = -0.700 m/s^2 (deceleration)
First, we need to determine the final velocity after 1.00 minute. Since the engine is turned off, the deceleration remains constant, so we can use the equation:
v = u + at
where:
t = time
Given:
t = 1.00 minute = 60 seconds
v = 95.0 m/s + (-0.700 m/s^2)(60 s)
v = 95.0 m/s - 42.0 m/s = 53.0 m/s
Now, let's substitute the values into the distance formula to find the distance traveled:
d = (v^2 - u^2) / (2a)
d = (53.0 m/s)^2 - (95.0 m/s)^2 / (2(-0.700 m/s^2))
d = 2809.0 m^2/s^2 - 9025.0 m^2/s^2 / (-1.4 m/s^2)
d = -6216.0 m^2/s^2 / (-1.4 m/s^2)
d = 4440.0 m
Therefore, the airplane will travel a distance of 4440 meters in 1.00 minute.
To find the distance traveled by the airplane, we can use the equation of motion:
d = v0 * t + (1/2) * a * t^2
Where:
d is the distance traveled,
v0 is the initial velocity,
a is the acceleration, and
t is the time elapsed.
Given:
Initial velocity, v0 = 95.0 m/s
Acceleration, a = -0.700 m/s^2
Time, t = 1.00 minute = 60 seconds
Now, let's plug in the values into the equation:
d = (95.0 m/s) * (60 s) + (1/2) * (-0.700 m/s^2) * (60 s)^2
First, calculate the first part of the equation:
v0 * t = (95.0 m/s) * (60 s) = 5700 m
Next, calculate the second part of the equation:
(1/2) * a * t^2 = (1/2) * (-0.700 m/s^2) * (60 s)^2 = -1260 m
Now, add the two parts together to get the total distance:
d = 5700 m + (-1260 m) = 4440 m
Therefore, the airplane will travel a distance of 4440 meters in 1.00 minute. So, your answer of 4440m is correct!