A gun fires a bullet vertically into a 1.40-kg block of wood at rest on a thin horizontal sheet.?

Question

If the bullet has a mass of 27.8 g and a speed of 230 m/s , how high will the block rise into the air after the bullet becomes embedded in it?PLEASE HELP! i used the equation for conservation of momentum and I keep getting 106m...theres no way thats right! ð

Hermina Ferry · Accepted Answer

If the bullet has a mass of 27.8 g and a speed of 230 m/s , how high will the block rise into the air after the bullet becomes embedded in it? gun fires a bullet vertically into a 1.40-kg block of wood at rest on a thin horizontal sheet.?Letâs use the following equation to determine the initial momentum.M = 0.0278 * 230 = 6.394Total mass = 0.0278 + 1.4 = 1.4278 kg Final momentum = 1.4278 * v1.4278 * v = 6.394v = 6.394 Ã· 1.4278This is approximately 4.478 m/s. As the block and bullet rise to their maximum height, their velocity deceases from this number to 0 m/s at the rate of 9.8 m/s each second. Letâs use the following equation to determine their maximum height. vf^2= vi^ 2 + 2 * a * d, vf = 0, a = -9.80 = (6.394 Ã· 1.4278)^2 + 2 * -9.8 * d19.6 * d = (6.394 Ã· 1.4278)^2d = (6.394 Ã· 1.4278)^2 Ã· 19.6 This is approximately 1.023 meters.

Hermina Ferry · Answer

M1V1 = -M2V2, to get the velocity the bullet in the wood will goV2= M1V1 (bullets momentum) / (M1+M2) (the masses stuck together)V2= (0.0278 x 230) / (1.4+0.0278), = 4.48 m/sNow there are many formulas we can use to get different values, but now that the wood and bullet are going up against gravity at that speed, the distance can be found by:(where r = displacement, u = initial velocity and the velocity at peak height, v, = 0 )V^2 - U^2 = 2ar1/2 x (0 - 4.48^2 / -9.8 ) = r r = 1.024 metres*As a bonus:*To check if your answer is right, you can use the formulamu1 + mu2 = mv1 + mv2and rearrange that formula for values you got at the start, for example, mu2 = 0, so to check it:mu2, 0, = mv1 + mv2 - mu1= 0.002So it is right. it is only not 0.0 due to small rounding off errors

Kelsie Sawayn

A gun fires a bullet vertically into a 1.40-kg block of wood at rest on a thin horizontal sheet.?

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