can someone help me in this problem?
a bullet is fired from a rifle, emerging from the muzzle at 340 meters per second. it strikes a sandbag some distance away, having lost 10 percent of its velocity due to air resistance. if it penetrates the sandbag to a depth of 12.0 centimeters, how long did it take for the bullet to come to rest in sandbag?
- WhomeLv 79 months agoFavorite Answer
Velocity entering the sandbag
v = 340(0.90)
v = 306 m/s
If we assume the bullet experiences constant acceleration while slowing down in the sandbag. (a rather large assumption)
v² = u² + 2as
0² = 306² + 2a(0.12)
a = -390150 m/s²
s = ½at²
t = √(2s/a)
t = √(2(0.12)/390150)
t = 7.84 x 10^-4 s
- SpacemanLv 79 months ago
vi = velocity when entering the sandbag = 0.9 x 340 m/s = 306 m/s
vf = final velocity = 0 m/s
d = distance traveled through sandbag = 12.0 cm = 0.12 m
t = elapsed time = to be determined
d = 0.5t(vi + vf)
2d = t(vi + vf)
2d/(vi + vf) = t
t = 2d/(vi + vf)
t = (2 x 0.12 m)/(306 m/s + 0 m/s)
t = 0.000784314 s = 0.784 ms
- electron1Lv 79 months ago
10% of 340 is 34 m/s. To determine the bullet’s velocity before hitting the sandbag, subtract these to velocities.
v = 340 – 34 = 306 m/s
As the bullet moves a distance of 0.12 meter, its velocity decreases to 0 m/s. Let’s use the following equation to determine the acceleration.
vf^2 = vi^2 + 2 * a * d
0 = 306^2 + 2 * a * 0.12
a = -93,636 ÷ 0.24 = -390,150 m/s^2
Let’s use the following equation to determine the time.
vf = vi + a * t
0 = 306 – 390,150 * t
t = 306 ÷ 390,150
This is approximately 7.84 * 10^-4 seconds.
- oubaasLv 79 months ago
impact speed V = Vo*0.9 = 340-34 = 306 m/sec
V aver = V/2 = 153 m/sec
time t = d/Vaver = 120/153 = 0.784 m/sec (784 μsec)
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- daniel gLv 79 months ago
The steps to solve this is to calculate the projectile velocity at the point it hits the sand bag.
The next step is knowing the stopping distance, you calculate the deceleration in the sand bag.
From that, you can calculate the time it took for the projectile to stop.
One secret to making such math problems easy is learning and knowing how to work and solve a problem to solution. The numbers don't mean anything, those can be variable.
Focus more on working the problem instead of dwelling on numbers.
Not that hard when you understand this.
I will let you work the numbers to solution, If I give you answers, you don't learn anything.
- 9 months ago
Not long at all...rather quicky