Question

A 5.5 g dart is Fired into a block of wood with a mass of 22.6g. The wood block is initially at rest on a 1.5m tall post. After the collision, the wood block and dartland 2.5 m from the base of the post. What is the initial speed of the dart?

Answer 1

use kinematics first, to find the time the block and dart were in the air
x = x(initial) + .5at^2 *finding using the y component, so v initial would be 0
0 = 1.5 + (.5)(-9.8)t^2
t= .553 seconds
plugging that into the same equation, modified a bit
x = x(initial) + v(initial)t *no acceleration due to gravity, we are using x component
2.5 = 0 + v(.553)
v = 4.51 m/s of the block and dart
Now we use conservation of momentum
mv(dart) + mv(block) = (m1 + m2)v
(.0055)v + 0 = (.0055 + .0226)(4.51)
v= 23.042 m/s was initial speed of dart