an arresting device on a carrier deck stops an airplane in 1.5s. the avg. acceleration was 49 m/s2. what was the stopping distance? what was the initial speed? so i think v2=0, t=1.5, a= 49, so i need d and v1. i got v1=73.5 m/sec and d= 55 m. i took 0=v1-49(1.5) to get that v1. and also 73.5(1.5)-1/2 (49) (1.5)^2 to get d=55.12 m. Is this correct?
d=1/2 a t^2=1/2*49*1.5^2
correct.
i am not sure
Your calculation for the initial speed and stopping distance is almost correct. However, there is a small mistake in your calculation for the stopping distance.
To calculate the stopping distance (d), you can use the equation:
d = v1 * t + (1/2) * a * t^2
Given:
t = 1.5 s
a = 49 m/s^2
v2 = 0 (final velocity)
Using the formula and substituting the given values, we get:
0 = v1 * 1.5 + (1/2) * 49 * (1.5)^2
0 = v1 * 1.5 + (1/2) * 49 * 2.25
0 = v1 * 1.5 + 54.5625
v1 * 1.5 = -54.5625
v1 = -54.5625 / 1.5
v1 = -36.375 m/s (initial speed)
To find the stopping distance (d):
d = v1 * 1.5 + (1/2) * 49 * (1.5)^2
d = -36.375 * 1.5 + (1/2) * 49 * 2.25
d = -54.5625 + 54.5625
d = 0 m
So, the initial speed is -36.375 m/s and the stopping distance is 0 m.
To find the stopping distance and initial speed in this scenario, you can apply the equations of motion. Here's a step-by-step breakdown of how to get to the answers:
1. Use the equation of motion: v2 = v1 + at, where v2 is the final velocity (0 m/s), v1 is the initial velocity (unknown), a is the acceleration (-49 m/s^2), and t is the time (1.5 s).
Rearranging the equation, you get v1 = v2 - at.
Substituting the values:
v1 = 0 - (-49 m/s^2 * 1.5 s)
v1 = 73.5 m/s
So, you correctly found the initial speed to be 73.5 m/s.
2. To calculate the stopping distance, you can use the equation of motion for displacement: d = v1t + (1/2)at^2, where d is the displacement (unknown).
Rearranging the equation, you get d = v1t - (1/2)at^2.
Substituting the values:
d = (73.5 m/s * 1.5 s) - (1/2) * (-49 m/s^2) * (1.5 s)^2
d = 110.25 m - 55.125 m
d = 55.125 m
So, the stopping distance you found, 55.12 m, was correct.
However, the initial speed you calculated is slightly off. It should be v1 = 73.5 m/s, not 73.5 m/sec. Besides that, your calculations are accurate.