D = distance between th two trains at the start of the motion = 100 miles
V = speed of the faster train towards slower train = 60 mph
v = speed of the slower train towards faster train = 40 mph
t = time taken by the two trains to collide = ?
time taken by the two trains to collide is given as
t = D/(V + v)
t = 100/(60 + 40) = 1 h
v' = speed of the bird = 90 mph
d = distance traveled by the bird
distance traveled by the bird is given as
d = v' t
d = 90 x 1
d = 90 miles
Answer: Truck 2, because it has a larger mass than truck 1 (and the same velocity)
Explanation:
We can write the kinetic energy of an object with mass M and velocity V as:
K = (M/2)*V^2
Let's calculate the kinetic energy for each truck:
Now, we can see that both trucks move at the same velocity, but truck 1 has a mass of 5000 pounds, while truck 2 has also a mass of 5000 pounds and an extra of 900 pounds.
Then the total mass of truck 2 is 5000 pounds + 900 pounds = 5900 pounds.
Then both trucks have the same velocity, and truck 2 has a larger mass than truck 1, this implies that truck 2 will have a larger kinetic energy than truck 1.
Using the formula:
w = m x g ....... eq1
here w is weight of the object.
m is mass of the object, and
g is the acceleration of gravity.
mass, m = 14 lbm (given)
acceleration of gravity, g= 32.0 ft/
Now, substituting the values in equation (1):
w = 14lbm x 32.0 ft/ = 448 lbm ft/
since, 1 lbf = 32.174 lbm ft/
so, w = 448 x
w = 13.924lbf
Hence, the mass of an object is 13.924 lbf.
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Answer:
a) the final velocity is 35.75 ft/s
b) The final elevation is 45 ft
Explanation:
Given the data in the question;
Weight of object; W = 100 lbf
Change in kinetic energy; ΔE = 500 ft-lb
so
m - m = ΔE
m - m = 500
multiply both sides by 2
m - m = 1000
m( - ) = 1000
- = 1000/m
- = (1000)(g) / W
we know that, acceleration due to gravity g = 9.8 m/s² = 32.18 ft/s²
so we substitute
- = (1000)(32.18) / 100
- = (1000)(32.18) / 100
- = 32180 / 100
- = 321.8
since The initial velocity is given to be 40 ft/s;
(40)² - = 321.8
1600 - = 321.8
= 1600 - 321.8
= 1278.2
= √1278.2
= 35.75 ft/s
Therefore, the final velocity is 35.75 ft/s
b)
we know that;
change in potential energy is;
ΔP.E = mg( h - h )
given that; increase in potential energy; ΔP.E = 1500 ft-lbf
and mg = Weight = 100 lbf
we substitute
1500 = 100( h - h )
h - h = 1500 / 100
h - h = 15 ft
given that, elevation of the object; h = 30 ft
h - 30 ft = 15 ft
h = 15 ft + 30 ft
h = 45 ft
Therefore, The final elevation is 45 ft