Two radio antennas A and B radiate in phase. Antenna B is a distance of 120 m to the right of antenna A. Consider point Q along
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Answer:
The maximum height reached by the two blocks is approximately 0.1147959 × v₀²
Explanation:
The mass of block B = m
The mass of block A = 3·m
The initial velocity of block B, v₂ = 0 m/s
The initial velocity of block A, v₁ = v₀
The amount of friction between the blocks and the surface = Negligible friction
By the Law of conservation of linear momentum, we have;
Total initial momentum = Total final momentum
3·m·v₁ + m·v₂ = (3·m + m)·v₃ = 4·m·v₃
Plugging in the values for the velocities gives;
3·m × v₀ + m × 0 = (3·m + m)·v₃ = 4·m·v₃
∴ 3·m × v₀ = 4·m·v₃
The kinetic energy, K.E. of the combined blocks after the collision is given as follows;
K.E. = 1/2 × mass × v²
The potential energy, P.E., gained by the two blocks at maximum height = The kinetic energy, K.E., of the two blocks before moving vertically upwards
The potential energy, P.E. = m·g·h
Where;
m = The mass of the object at the given height
g = The acceleration due to gravity
h = The height at which the object of mass, 'm', is located
Therefore, for h = The maximum height reached by the two blocks, we have;
P.E. = K.E.
The maximum height reached by the two blocks, h ≈ 0.1147959·v₀².
v =
and
a =
We have acceleration and velocity so:
3 =
88.3 =
In the acceleration equation we can isolate for v and then plug it back into the other equation to solve...
So...
Divide by three and
t = 29.4 s
Answer:
The answer to the question is
The ball will go 0.14 meters high if the gun is aimed vertically
Explanation:
The energy in the spring → Energy, E =
Where E = energy in the spring
k = Spring constant
x = Spring compression or stretch
Therefore E =
The spring energy is transferred to the ball as kinetic energy based on the first law of thermodynamics which states that energy is neither created nor destroyed
Kinetic energy = KE =
From which v = =
= 1.66 m/s
from v² =u² - 2·a·S
Where v = final velocity = 0 m/s
u = initial velocity = 1.66 m/s
a = g = Acceleration due to gravity
S = height
Therefore 0 = 1.66² - 2×9.81×S
or S = 1.66² ÷ (2×9.81) = 0.14 m