An eraser falls out of your back pack while you are walking down the hall. You are walking at a speed of 0.2 m/s and the distance from the backpack to the floor is 1 meter.
a) How long does it take for the eraser to hit the ground?
b) What is the vertical velocity of the eraser just before it hits the ground?
c) Estimate the average acceleration during the collision with the floor. State all assumptions.
d) Draw a vertical velocity vs time graph of the eraser. What is the acceleration of the eraser before it hits the floor?
What I have:
a) y= (v-initialofy)(t) + 0.5a(t^2)
-1 = (0)t + 0.5(-9.8)(t^2)
t = 0.45 seconds
b) Vy = (v-initialofy) + (accelerationofy)(t) = 0 + (-9.8)(0.45) = -4.427 m/s^2
c) Average acceleration should be -9.8 m/s^2 because that is a constant that does not change. I don't know what the assumptions are - would appreciate some help with that.
d) I need help with the graph. The acceleration should still be -9.8 m/s^2 because that is a constant
I will comment on your answers:
a) Looks good!
b) is fine, except that the result should have units of velocity.
c) The average acceleration during the collision is $\frac{\Delta v}{\Delta t}$. You know $\Delta v$, as the initial velocity $v_i$ is the one from b) and the final velocity $v_f$ is zero (making the crude assumption that it doesn't bounce back up). Now all you need to do is estimate $\Delta t$, which should be pretty small.
A alternative, more realistic, set of assumptions would be that the rubber bounced back up to, say, $0.5$ meters. Figure out which speed $v_b$ the rubber must have had when bouncing off of the floor to reach this height, and use it in the formula for the average above ($\Delta v=v_b-v_i$, but remember the signs of these!).
d) The function for the velocity is the derivative of the function for the position, so it will be linear. But think about what happens at and after the bounce.