Answer:
θ₀ = 84.78° (OR) 5.22°
Explanation:
This situation can be treated as projectile motion. The parameters of this projectile motion are:
R = Range of Projectile = 150 m
V₀ = Launch Speed of Projectile = 90 m/s
g = 9.8 m/s²
θ₀ = Launch angle (OR) Angle of Elevation = ?
The formula for range of a projectile is given as:
R = V₀² Sin 2θ₀/g
Sin 2θ₀ = Rg/V₀²
Sin 2θ₀ = (150 m)(9.8 m/s²)/(90 m/s)²
2θ₀ = Sin⁻¹ (0.18)
θ₀ = 10.45°/2
<u>θ₀ = 5.22°</u>
Also, we know that for the same launch velocity the range will be same for complementary angles. Therefore, another possible value of angle is:
θ₀ = 90° - 5.22°
<u>θ₀ = 84.78°</u>
Answer:
C) 6 m/s
Explanation:
Given that
m₁=5000 kg
The initial velocity of 5000 kg car =u₁
m₂=10,000 kg
The initial velocity of 10000 kg car =u₂ = 0 m/s
After collision the final speed of the both car,v = 2 m/s
There is no any external force on the system that is why linear momentum will be conserved.
Linear momentum P = m v
m₁u₁ + m₂u₂ = (m₂ + m₁) v
5000 x u₁ + 10000 x 0 = (5000 + 10000) x 2
5000 x u₁ = 15000 x 2
5 x u₁ = 15 x 2
u₁ = 6 m/s
Therefore the answer is C.
C) 6 m/s
Question:
The operations manager for a well-drilling company must recommend whether to build a new facility, expand his existing one, or do nothing. He estimates that long-run profits (in $000) will vary with the amount of precipitation (rainfall) as follows:
Alternative Precipitation
Low Normal High
Do nothing -100 100 300
Expand 350 500 200
Build new 750 300 0
If he feels the chances of low, normal, and high precipitation are 30 percent, 20 percent, and 50 percent respectively, What is EVPI (Expected value of Perfect Information)?
A. $140,000
B. $170,000
C. $285,000
D. $305,000
E. $475,000
Answer:
D. $170,000
Explanation:
The expected long run profits are for
Low Normal High
Do nothing -100*0.3 100*0.2 300*0.5 = 140
Expand 350*0.3 500*0.2 200*0.5 = 305
Build new 750*0.3 300*0.2 0*0.5 = 285
Therefore the expected long run profits are
$140,000
$305,000
$285,000
Based on his selected option being either to build new or to expand, the most profitable option is to expand
=$305,000
EVPI = EPPI-EMV =$170,000
The answer is bend towards normal.
