A model railroad train travels at a constant speed of 8 cm/s . How far would the train travel in one minute ?
1 answer:
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Answer:
The arrow is at a height of 500 feet at time t = 2.35 seconds.
Explanation:
It is given that,
An arrow is shot vertically upward at a rate of 250 ft/s, v₀ = 250 ft/s
The projectile formula is given by :
We need to find the time(s), in seconds, the arrow is at a height of 500 ft. So,
On solving the above quadratic equation, we get the value of t as, t = 2.35 seconds
So, the arrow is at a height of 500 feet at time t = 2.35 seconds. Hence, this is the required solution.
1) 9.4 m/s
First of all, we can calculate the work done by the horizontal force, given by
W = Fd
where
F = 34.6 N is the magnitude of the force
d = 12.9 m is the displacement of the cart
Solving ,
W = (34.6 N)(12.9 m) = 446.3 J
According to the work-energy theorem, this is also equal to the kinetic energy gained by the cart:
Since the cart was initially at rest, , so
(1)
where
m is the of the cart
v is the final speed
The mass of the cart can be found starting from its weight, :
So solving eq.(1) for v, we find the final speed of the cart:
2)
The work done on the train is given by
W = Fd
where
F is the magnitude of the force
d is the displacement of the train
In this problem,
So the work done is
3)
According to the work-energy theorem, the change in kinetic energy of the train is equal to the work done on it:
where
W is the work done
is the change in kinetic energy
Therefore, the change in kinetic energy is
4) 37.2 m/s
According to the work-energy theorem,
where
is the final kinetic energy of the train
is the initial kinetic energy of the train, which is zero since the train started from rest
Re-writing the equation,
where
m = 36300 kg is the mass of the train
v is the final speed of the train
Solving for v, we find