Assuming the top of the garbage can is 43 m below the roof.
Acceleration due to gravity, a = -g = -9.8 m/s/s
Distance, S = -43 m
initial velocity, u = 0 m/s
final velocity, v
v²-u²=2aS
v=sqrt(2aS+u²)
=sqrt(2*(-9.8)*(-43))
=29.03 m/s
For impact with garbage can,
u=29.03 m/s
v=0
S=-0.457 m
Using the same formula
v²-u²=2aS
Can you find the acceleration a?
A very silly person, intent on catching pigeons on the roof of an apartment building, trips and falls a distance of 43.0 m. She lands on a metal garbage can, crushing it to a depth of 0.457 m and walks away without having been seriously hurt. What acceleration did she experience during the collision?
6 answers
The acceleration is 922 m/s^2.
How come v=0 in the final equation? I thought that v represented the velocity at impact rather than the velocity after the girl lands.
How come v=0 in the final equation? I thought that v represented the velocity at impact rather than the velocity after the girl lands.
I was using the same terminology, namely
u=initial, v=final,
that is why v=0 for the decceleration part.
u=initial equals the velocity attained during the free-fall, namely 29.03 m/s as indicated.
922 m/s/s is correct, considering that it took 43 m to accelerate to 29 m/s, and is reduced to zero in 0.457 m.
u=initial, v=final,
that is why v=0 for the decceleration part.
u=initial equals the velocity attained during the free-fall, namely 29.03 m/s as indicated.
922 m/s/s is correct, considering that it took 43 m to accelerate to 29 m/s, and is reduced to zero in 0.457 m.
I don't understand how you got that the acceleration is 922 m/s/s. I've been trying to understand it for a long time and it's not making sense.
I will rephrase the last part:
For impact with garbage can,
Velocity on impact with garbage can, u = 29.03 m/s
Final velocity (at rest), v = 0
Displacement, equal to denting of garbage can, S = -0.457 m
Using the same formula
v²-u²=2aS
a=(v²-u²)/2S
=(0²-29.03²)/(2*0.457)
=842.74/(.914)
=922.0 m/s/s
For impact with garbage can,
Velocity on impact with garbage can, u = 29.03 m/s
Final velocity (at rest), v = 0
Displacement, equal to denting of garbage can, S = -0.457 m
Using the same formula
v²-u²=2aS
a=(v²-u²)/2S
=(0²-29.03²)/(2*0.457)
=842.74/(.914)
=922.0 m/s/s
Hello.
I was just wondering...
Since the question said "She lands on a metal garbage can, crushing it to a depth of 0.457 m", how did you know that final depth of the garbage can was equal to the negative displacement caused by crushing?
I was just wondering...
Since the question said "She lands on a metal garbage can, crushing it to a depth of 0.457 m", how did you know that final depth of the garbage can was equal to the negative displacement caused by crushing?