A steam catapult launches a jet aircraft from the aircraft carrier John C. Stennis, giving it a speed of 205 mi/h in 2.70 s.
(a) Find the average acceleration of the plane.
(b) Assuming the acceleration is constant, find the distance the plane moves.
To find the average acceleration of the plane, we can use the formula:
average acceleration = (final velocity - initial velocity) / time
Given:
- Initial velocity (v0) = 0 mph (as the plane starts from rest)
- Final velocity (v) = 205 mph
- Time (t) = 2.70 s
(a) Average Acceleration:
average acceleration = (205 mph - 0 mph) / 2.70 s
average acceleration = 205 mph / 2.70 s
average acceleration = 75.93 mph/s
Therefore, the average acceleration of the plane is 75.93 mph/s.
To find the distance the plane moves assuming constant acceleration, we can use the formula:
distance = initial velocity * time + (1/2) * acceleration * time^2
Given:
- Initial velocity (v0) = 0 mph
- Time (t) = 2.70 s
- Acceleration (a) = 75.93 mph/s (from part a)
(b) Distance:
distance = 0 mph * 2.70 s + (1/2) * 75.93 mph/s * (2.70 s)^2
distance = 0 + (1/2) * 75.93 mph/s * 7.29 s^2
distance = 0 + 0.5 * 75.93 mph/s * 7.29 s^2
distance = 0 + 0.5 * 552.5043 mph * s
distance = 0 + 276.25215 mph * s
Therefore, the distance the plane moves assuming constant acceleration is 276.25215 mph * s.
To find the average acceleration of the jet aircraft launched by the steam catapult, we can use the formula:
acceleration = change in velocity / time
Given:
Initial velocity (u) = 0 mi/h (since the aircraft starts from rest)
Final velocity (v) = 205 mi/h
Time (t) = 2.70 s
(a) Average acceleration:
acceleration = (v - u) / t
acceleration = (205 mi/h - 0 mi/h) / 2.70 s
acceleration = 205 mi/h / 2.70 s
To solve this, we need to convert the units so that the time is measured in seconds rather than hours:
1 mi/h = 0.44704 m/s
1 h = 3600 s
Therefore,
acceleration = (205 mi/h / 2.70 s) × (0.44704 m/s) / (1 mi/h) × (3600 s / 1 h)
Simplifying the units, we get:
acceleration = (205 × 0.44704) / (2.70 × 3600) m/s²
Now we can calculate the value:
acceleration ≈ 8.41 m/s²
Hence, the average acceleration of the plane is approximately 8.41 m/s².
(b) To find the distance the plane moves, we can use the formula:
distance = initial velocity × time + (1/2) × acceleration × time²
Given:
Initial velocity (u) = 0 mi/h
Time (t) = 2.70 s
Acceleration (a) = 8.41 m/s²
We need to convert the units before using the formula:
Initial velocity = 0 mi/h × 0.44704 m/s / (1 mi/h)
Initial velocity = 0 m/s
Plugging in the values, we get:
distance = (0 m/s) × (2.70 s) + (1/2) × (8.41 m/s²) × (2.70 s)²
Simplifying the equation:
distance = 0 + (1/2) × 8.41 m/s² × 7.29 s²
Now we can calculate the distance:
distance ≈ 27.2 m
So, assuming the acceleration is constant, the plane moves approximately 27.2 meters.
I guess we are to do this all in feet and seconds?
v = 205 mi/h *5280ft/mi*(1h/3600s))
= 301 ft/s
a = 301/2.7 = 111 ft/s^2
d = (1/2)(111)(2.7)^2
=406 ft