Answer:
d) g/2
Explanation:
We need to use one of Newton's equations of motion to find the position of the stone at any time t.
x(t) = x₀(t) + ut - ¹/₂at²
Where
x₀(t) = initial position of the stone.
x(t) - x₀(t) = distance traveled by the stone at any time.
u = initial velocity of the stone
a = acceleration of the stone
t = time taken
On both planets, before the stone was thrown by the astronaut, x = 0 and t = 0.
=> 0 = x₀(t)
=> x₀(t) = 0
On earth, when the stone returns into the hand of the astronaut at time T on earth, x = 0.
=> 0 = 0 + uT - ¹/₂gT² (a = g)
=> uT = ¹/₂gT²
=> g = 2u/T
On planet X, when the stone returns into the hand of the astronaut, time = 2T , x = 0.
=> 0 = 0 + u(2T) - ¹/₂a(2T)²
=> 2uT = 2aT²
=> a = u/T
By comparing we see that a = g/2.
Answer:
Option C. 210 J.
Explanation:
From the question given above, the following data were obtained:
Mass (m) = 0.75 Kg
Height (h) = 12 m
Velocity (v) = 18 m/s
Acceleration due to gravity (g) = 9.8 m/s²
Total Mechanical energy (ME) =?
Next, we shall determine the potential energy of the plane. This can be obtained as follow:
Mass (m) = 0.75 Kg
Height (h) = 12 m
Acceleration due to gravity (g) = 9.8 m/s²
Potential energy (PE) =?
PE = mgh
PE = 0.75 × 9.8 × 12
PE = 88.2 J
Next, we shall determine the kinetic energy of the plane. This can be obtained as follow:
Mass (m) = 0.75 Kg
Velocity (v) = 18 m/s
Kinetic energy (KE) =?
KE = ½mv²
KE = ½ × 0.75 × 18²
KE = ½ × 0.75 × 324
KE = 121.5 J
Finally, we shall determine the total mechanical energy of the plane. This can be obtained as follow:
Potential energy (PE) = 88.2 J
Kinetic energy (KE) = 121.5 J
Total Mechanical energy (ME) =?
ME = PE + KE
ME = 88.2 + 121.5
ME = 209.7 J
ME ≈ 210 J
Therefore, the total mechanical energy of the plane is 210 J.
Answer:
magnitude:
formula: v=√(x)^2 + (y)^2 + (z)^2
√(2.5)^2 +(3)^2 + (7.8)^2
√76.09
=8.7
I hope this helped :)
Answer:
Newton's third law of motion.
Explanation:
We are told the force needed to throw the full soda can was more than that needed to throw the empty can.
Now, the weight of the full soda can will be more than that of the empty can. Therefore, the full can will demand more force than that of the empty can due to Newton's third law of motion which states that to every action, there is an equal and opposite reaction.
Answer:
1. 10.5 Kg
2. s/g
Explanation:
1. Determination of the mass of gasoline
Density of gasoline = 0.7 Kg/L
Volume of gasoline = 15 L
Mass of gasoline =?
The density of a substance is simply defined as the mass of the substance per unit volume of the substance. Mathematically, the density of a substance can be expressed as:
Density = mass / volume
With the above formula, we can obtain the mass of the gasoline as follow:
Density of gasoline = 0.7 Kg/L
Volume of gasoline = 15 L
Mass of gasoline =?
Density = mass / volume
0.7 = Mass of gasoline / 15
Cross multiply
Mass of gasoline = 0.7 × 15
Mass of gasoline = 10.5 Kg
2. Density has various units some are listed below:
I. Kilogram per litre (Kg/L)
II. Kilogram per cubic metre (Kg/m³)
III. Milligram per millilitre (mg/mL)
IV. Gram per millilitre (g/mL)
V. Gram per cubic centimetre (g/cm³)
Considering the options given in the question above, it is evident that second per gram (s/g) is not a unit of density because density is mass per unit volume.
