Answer:
1) The maximum height reached is approximately 39.715 m
2) The time it takes the ball to reach the its highest point is approximately 2.85 s
Explanation:
1) The vertical velocity of the ball, u = 27.9 m/s
The acceleration due gravity, g = 9.8 m/s²
The kinematic equation that gives the height, h, reached by the ball is given as follows;
v² = u² - 2·g·h
Where;
v = The final velocity of the ball = 0 m/s at the maximum height
h = The height reached by the ball = at maximum height
Therefore, by substitution of the known values, we have;
v² = u² - 2·g·h
0² = 27.9² - 2 × 9.8 ×
2 × 9.8 × = 27.9²
= 27.9²/(2×9.8) ≈ 39.715
The maximum height reached = ≈ 39.715 m
2) From the kinematic equation of motion, v = u - g·t, we have the time, t, it takes the ball to reach the maximum height given as follows
At maximum height, the final velocity, v = 0 m/s, therefore, we have;
0 = 27.9 - 9.8 × t
9.8 × t = 27.9
t = 27.9/9.8 ≈ 2.85
The time it takes the ball to reach the maximum height = t ≈ 2.85 seconds.
Answer:
Conservation of energy
Explanation:
The first law of thermodynamics is given by :
Here,
Q is amount of heat added to the system
is change in internal energy
W is amount of work done by the system
It is clear that the energy can be neither created nor destroyed, it remains conserved. Hence, first law of thermodynamics shows that conservation of energy.
a) The initial speed of the bullet is 330.5 m/s
b) The collision is inelastic
c) The impulse is -2.97 kg m/s
Explanation:
a)
The energy lost by the block while sliding (which is equal to the work done by friction) is equal to the kinetic energy of the block after the bullet has been embedded into it, therefore we can write
where
M = 1.20 kg is the mass of the block
m = 9.00 g = 0.009 kg is the mass of the bullet
v is the combined speed of bullet+block after the collision
is the coefficient of friction
is the acceleration of gravity
d = 0.310 m is the distance through which the block slides
Solving for v,
This is the final velocity of the block+bullet after the collision.
Now we can apply the law of conservation of momentum: in fact, the total momentum of the system before the collision must be equal to the total momentum after the collision, so we get
where
u is the initial velocity of the bullet
U = 0 is the initial velocity of the block (initially at rest)
v = 2.46 m/s
Solving for u,
b)
To check whether the collision is elastic or inelastic, we just need to compare the total kinetic energy before and after the collision.
Before the collision, we have:
While after the collision
We see that the final kinetic energy is less than the initial kinetic energy: therefore, the collision is inelastic, since part of the energy has been converted into other forms of energy (e.g. thermal energy).
c)
The impulse of the block is equal to its change in momentum, so:
where
v' = 0, since the block comes to a stop
v = 2.46 m/s is the velocity of the block just after the collision
Substituting,
And the impulse is negative, because its direction is opposite to the direction of motion of the block (this means that the force exerted on the block, which is the force of friction, acts in the direction opposite to the motion of the block).
Learn more about kinetic energy and momentum:
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Answer:
L = 3.51
Explanation:
Pendulum equation is T = 2pi
T = 1.5 and we are solving for L
1.5=2
square both sides to get 2.25 = 2
multiply both sides by 9.81 then divide by 2 and 3.14 as a substitue for pi. The answer should be about 3.51 in length
L = 3.51
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