posted by Robert C .
An arrow is fired with a speed of 20.0 m/s at a block of Styrofoam resting on a smooth surface. The arrow penetrates a certain distance into the block before coming to rest relative to it. During this process the arrow's deceleration has a magnitude of 1300 m/s2 and the block's acceleration has a magnitude of 450 m/s2
(a) How long does it take for the arrow to stop moving with respect to the block?
(b) What is the common speed of the arrow and block when this happens?
(c) How far into the block does the arrow penetrate?
(a) Because the arrow's deceleration and block's acceleration are acting in the same direction, add them to get a total acceleration of the arrow+styrofoam to be (-1300m/s2)+(-450m/s2)=-1750m/s2. Using v=v0+at where v=0m/s (final velocity of arrow relative to block), v0= 20m/s, you get t=0.0114s
(b) The styrofoam block starts from v0=0m/s, has an acceleration of a=450m/s2, and t from part (a)=0.0114s, we plug into v=v0+at to find v=5.13m/s
(c) Using x=v0t+.5at2, v0=0m/s because the initial velocity of the arrow compared to the block is insignificant, a=1750m/s2 from part (a), and t=0.0114s from part (a) to give us x=0.1137m