Answer:
9.99
Explanation:
The value of (997)^1/3
(997)^1/3
997 = (1000 - 3)
(1000 - 3)^1/3
Expanding :
[1000(1 - 3/1000)]^1/3
1000^1/3 * (1 - 3/1000)^1/3
Cube root of 1000
10 * (1 - 3/1000 * 1/3)
10 * (1 - 1/1000)
10 * (1 - 0.001)
10(0.999)
= 9.99
Hence, the value of (997)^1/3 according to binomial theorem is 9.99
Answer:
μ = 0.535
Explanation:
On a level floor, normal force = weight.
N = W
Friction force = normal force × coefficient of friction.
F = Nμ
Substitute:
F = Wμ
83 = 155μ
μ = 0.535
Round as needed.
The bus and the truck have the same velocity.
Also, Valerie and Owen have the same velocity.
Answer:
h = v₀² / 2g
, h = k/4g x²
Explanation:
In this exercise we can use the law of conservation of energy at two points, the lowest, before the shot and the highest point that the mouse reaches
Starting point. Lower compressed spring
Em₀ = K = ½ m v²
Final point. Highest on the path
= U = mg h
As or no friction the energy is conserved
Em₀ = Em_{f}
½ m v₀²² = m g h
h = v₀² / 2g
We can also use as initial energy the energy stored in the spring that will later be transferred to the mouse
½ k x² = 2 g h
h = k/4g x²
Answer: 6.48m/s
Explanation:
First, we know that Impulse = change in momentum
Initial velocity, u = 19.8m/s
Let,
Velocity after first collision = x m/s
Velocity after second collision = y m/s
Also, we know that
Impulse = m(v - u). But then, the question said, the guard rail delivered a "resistive" impulse. Thus, our impulse would be m(u - v).
5700 = 1500(19.8 - x)
5700 = 29700 - 1500x
1500x = 29700 - 5700
1500x = 24000
x = 24000/1500
x = 16m/s
Also, at the second guard rail. impulse = ft, so that
Impulse = 79000 * 0.12
Impulse = 9480
This makes us have
Impulse = m(x - y)
9480 = 1500(16 -y)
9480 = 24000 - 1500y
1500y = 24000 - 9480
1500y = 14520
y = 14520 / 1500
y = 9.68
Then, the velocity decreases by 3.2, so that the final velocity of the car is
9.68 - 3.2 = 6.48m/s
