A 1000-kg aircraft going 25 m/s collides with a 1500-kg aircraft that is parked. They stick together after the collision and are moving at 10 m/s. If they skid for 30 seconds before stopping, how far (in meters) did they skid?
Hint: Are the aircraft moving at a constant velocity after the collision or do they experience an acceleration?
After the collision, the two aircraft stick together and move with a constant velocity of 10 m/s. Since they are moving at a constant velocity, they do not experience any acceleration.
To find the distance they skid, we can use the formula:
Distance = Velocity x Time
In this case, the velocity is 10 m/s and the time is 30 seconds. Plugging these values into the formula, we have:
Distance = 10 m/s x 30 s
Calculating this, we get:
Distance = 300 meters
Therefore, the two aircraft skid for a distance of 300 meters before stopping.
In order to determine the distance the aircraft traveled during the skid, we need to consider their initial velocity, final velocity, and the time it took for them to stop.
First, let's calculate the initial momentum (p_initial) of each aircraft using the formula: p = m * v, where p is momentum, m is mass, and v is velocity.
For the 1000-kg aircraft:
p_initial1 = m1 * v1 = 1000 kg * 25 m/s = 25000 kg·m/s
The parked aircraft is not moving, so its initial momentum is zero:
p_initial2 = m2 * v2 = 1500 kg * 0 m/s = 0 kg·m/s
Since momentum is conserved during the collision and the two aircraft stick together, their total momentum after the collision (p_final) is the sum of their initial momenta:
p_final = p_initial1 + p_initial2 = 25000 kg·m/s + 0 kg·m/s = 25000 kg·m/s
After the collision, the combined mass of the two aircraft is:
m = m1 + m2 = 1000 kg + 1500 kg = 2500 kg
To find their final velocity after the collision, we can use the equation: p_final = m * v_final
25000 kg·m/s = 2500 kg * v_final
Therefore, the final velocity is:
v_final = 25000 kg·m/s / 2500 kg = 10 m/s
Now, to calculate the total distance traveled during the skid, we can use the equation: d = v_avg * t, where d is distance, v_avg is average velocity, and t is time.
Since the aircraft are decelerating from 10 m/s to 0 m/s during the skid, the average velocity is:
v_avg = (v_initial + v_final) / 2 = (10 m/s + 0 m/s) / 2 = 5 m/s
Given the total time of 30 seconds, we can calculate the distance:
d = v_avg * t = 5 m/s * 30 s = 150 meters
Therefore, the aircraft skid for a distance of 150 meters before stopping.
if acceleration is constant their average speed during the stop
= 10/2 = 5 m/s
5 m/s * 30 s = 150 meters
Motion is accelerated cause it says "If they skid for 30 seconds before stopping".
1) One should use a = Vf - Vo / t in order to find acceleration.
2) Then use d= vf^2 - Vo^2 / 2a in order to find acceleration.
1) As Vo = 10 m/s; Vf = 0 m/s and t = 30 s then a = -0.333
2) Using the former values, d = 150.15 m (rounded a = -0.333)
*Employing all decimals d = 150 m