y = 75.9 m
Explanation:
y = -(1/2)gt^2 + v0yt + y0
If we put the origin of our coordinate system at the point where a body is launched, then y0 = 0.
y = -(1/2)(9.8 m/s^2)(3 s)^2 + (40 m/s)(3 s)
= -44.1 m + 120 m
= 75.9
The difference between the above velocities is that they exist in opposite direction of each other. or it can be said that they are negative vectors of each other.
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: 1.14 N
Explanation :
As any body submerged in a fluid, it receives an upward force equal to the weight of the fluid removed by the body, which can be expressed as follows:
Fb = δair . Vb . g = 1.29 kg/m3 . 4/3 π (0.294)3 m3. 9.8 m/s2
Fb = 1.34 N
In the downward direction, we have 2 external forces acting upon the balloon: gravity and the tension in the line, which sum must be equal to the buoyant force, as the balloon is at rest.
We can get the gravity force as follows:
Fg = (mb +mhe) g
The mass of helium can be calculated as the product of the density of the helium times the volume of the balloon (assumed to be a perfect sphere), as follows:
MHe = δHe . 4/3 π (0.294)3 m3 = 0.019 kg
Fg = (0.012 kg + 0.019 kg) . 9.8 m/s2 = 0.2 N
Equating both sides of Newton´s 2nd Law in the vertical direction:
T + Fg = Fb
T = Fb – Fg = 1.34 N – 0.2 N = 1.14 N
Answer:
V = 26.95 cm³
Explanation:
Density is given by the formula :
ρ = m÷V
Density = mass ÷ Volume
Given both density and mass we rearrange, substitute and solve for Volume :
Rearranging the equation to make Volume the subject :
ρ = m÷V
ρV = m
V = m÷ ρ
Now substitute :
V = 45 ÷ 1.67
V = 26.9461077844
Take 2 decimal places as the density is 2 decimal places :
V = 26.95
Units will be cm³ as it is volume
Hope this helped and have a good day
