A bullet with a mass 0.05kg is speeding toward a block of mass 10kg. the bullet is initially moving with a velocity of 200m/s while the block is initially at rest....The bullet collides with the block, sticking inside, and knocks the block horizontally of the edge of a cliff. the cliff is 10m tall. how far from the cliff does the block (with bullet inside) land?
Use conservation of linear momentum to get the speed of the block with the bullet inside. Call that speed Vx
m*Vb = (M + m) Vx
M - block mass
m = bullet mass
Vb = bullet speed
Solve for Vx
Use the H = 10 m height of the building to compute the time the block takes to fall. Call that time T.
H = (g/2)T^2
Solve for T
The distance that the block lands away from the cliff if Vx * T
To determine how far from the cliff the block with the bullet inside lands, we can use the principles of physics and apply the conservation of energy.
Step 1: Calculate the initial kinetic energy of the bullet.
The kinetic energy (KE) of an object can be calculated using the formula KE = 0.5 * mass * velocity^2. For the bullet, with a mass of 0.05kg and an initial velocity of 200m/s:
KE_bullet = 0.5 * 0.05kg * (200m/s)^2
= 1000 J
Step 2: Determine the change in potential energy of the block-bullet system.
When the block with the bullet inside is lifted to the top of the 10m cliff, its potential energy increases. The change in potential energy can be calculated using the formula ΔPE = mass * gravity * height, where gravity is approximately 9.8 m/s^2.
ΔPE_block = 10kg * 9.8m/s^2 * 10m
= 980 J
Step 3: Applying the conservation of energy.
According to the conservation of energy principle, the initial kinetic energy of the system (bullet + block) is equal to the sum of their final potential energies when the block lands.
KE_bullet = ΔPE_block
1000 J = 980 J + ΔPE_cliff
To determine the change in potential energy of the cliff (ΔPE_cliff), we rearrange the equation:
ΔPE_cliff = 1000 J - 980 J
= 20 J
Step 4: Calculate the horizontal distance traveled by the block.
The potential energy converted to kinetic energy of the block-hammer system will be used to calculate the horizontal distance traveled. The horizontal distance is given by the formula d = (horizontal velocity)^2 / (2 * acceleration), where the acceleration is the acceleration due to gravity (9.8 m/s^2).
Using the equation ΔPE_cliff = KE_block:
ΔPE_cliff = 0.5 * mass * (horizontal velocity)^2
Substituting the values, we find:
20 J = 0.5 * 10kg * (horizontal velocity)^2
Simplifying, we have:
(horizontal velocity)^2 = (20 J * 2) / 10 kg
(horizontal velocity)^2 = 40 m^2/s^2
Taking the square root, we find:
horizontal velocity = √40 m/s
horizontal velocity ≈ 6.32 m/s
Now, we can calculate the horizontal distance:
d = (horizontal velocity)^2 / (2 * acceleration)
d = (6.32 m/s)^2 / (2 * 9.8 m/s^2)
d ≈ 2.58 m
Therefore, the block (with the bullet inside) will land approximately 2.58 meters away from the edge of the cliff.