3. A gun is fired vertically into a m . 1.38 kg block of wood at rest on nth in

Question

3. A gun is fired vertically into a m . 1.38 kg block of wood at rest on nth in horizontal sheet directly above it, as shown in the figure below. If the bullet has a mass of21.4 g and a speed of v = 300 m/s, how high will the block rise into the air after the bullet becomes embedded in it? 4. An astronaut of mass 82.2 kg is 25.4 m far out in space, with both the space ship and the astronaut at rest with respect to each other. Without a thruster, the only way to return to the ship is to throw his 0.494 kg wrench directly away from the ship. If be throws the wrench with a speed of 18.3 m/s, how many seconds does it take him to reach the ship?

Explanation / Answer

3)Solution- It's an inelastic collision.

By using conservation of momentum .
Let m be the bullet's mass and M the block's.
LetV1 is the initial bullet's mass and V2 the system's mass at the moment they launch off.
So,
mV1 = (M + m)V2
V2 = 21.4*300 / (1380 + 21.4) = 4.58m/s

Now using kinematics.
h = (V2)^2 / (2g)

=4.58^2/2*9.8

=1.07 m Answer

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