Part A:
Acceleration can be calculated by dividing the difference of the initial and final velocities by the given time. That is,
a = (Vf - Vi) / t
where a is acceleration,
Vf is final velocity,
Vi is initial velocity, and
t is time
Substituting,
a = (9 m/s - 0 m/s) / 3 s = 3 m/s²
<em>ANSWER: 3 m/s²</em>
Part B:
From Newton's second law of motion, the net force is equal to the product of the mass and acceleration,
F = m x a
where F is force,
m is mass, and
a is acceleration
Substituting,
F = (80 kg) x (3 m/s²) = 240 kg m/s² = 240 N
<em>ANSWER: 240 N </em>
Part C:
The distance that the sprinter travel is calculated through the equation,
d = V₀t + 0.5at²
Substituting,
d = (0 m/s)(3 s) + 0.5(3 m/s²)(3 s)²
d = 13.5 m
<em>ANSWER: d = 13.5 m</em>
Here,
height at failure, h1 = 525 m,
upward acceleration, a = 2.25 m/s^2,
velocity = v m/s,
<span>
SO, </span>
<span>
v^2 = 2*a*h = 2*2.25*525 = 2362.5 </span>
Now, acceleration, g = 9.8 m/s^2,
<span>
SO, </span>
<span>
heigt, h1 = v^2/2g = 2362.5 / 2*9.8 = 120.54 meters </span>
Hence,
<span>
a) </span>
Total height = 525+120.54 = 645.54 meters
b)
<span>time, for h1, t = v/g = sqrt(2362.5)/9.8 = 4.96 sec
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Given that the density of heptane is
The mass of heptane is
The density of water is
The mass of water is
The volume of heptane will be
The volume of water will be
Thus, the volume of heptane is 45.32 mL and the volume of water is 37 mL.
The total volume of liquid in the cylinder will be
The total volume of liquid in the cylinder will be 82.32 mL.
It will be 80 miles and it can be done only in 16 min
It's not so much a "contradiction" as an approximation. Newton's law of gravitation is an inverse square law whose range is large. It keeps people on the ground, and it keeps satellites in orbit and that's some thousands of km. The force on someone on the ground - their weight - is probably a lot larger than the centripetal force keeping a satellite in orbit (though I've not actually done a calculation to totally verify this). The distance a falling body - a coin, say - travels is very small, and over such a small distance gravity is assumed/approximated to be constant.
