Position: x = 18t y = 4t - 4.9t²
First derivative: x' = 18 y' = 4 - 9.8t
Second derivative: x'' = 0 y'' = - 9.8
Position vector: P = (18t) i + (4t - 4.9t²) j
Velocity vector: V = (18) i + (4 - 9.8t) j
Acceleration vector A = (- 9.8) j
Answer:
246.28 K
Explanation:
The total energy of one mole of gas molecules can be calculated by the formula given below
E = 
Where R is gas constant and T is absolute temperature.
Put the value of R as 8.314 and temperature as 245 , we get
E = 
= 3055.4 J
Add 16 j to it
Total energy of gas molecules = 3055.4 + 16 = 3071.4 J.
If T be the temperature after addition of energy then
= 3071.4
T =
T = 246.28 K
Explanation:
It is given that,
Uncertainty in the speed of an electron, 
According to Heisenberg uncertainty principle,
is the uncertainty in the position of an electron
Since, 
So, the uncertainty in its position is 
. Hence, this is the required solution.
Answer:
10.4 m/s
Explanation:
First, find the time it takes for the projectile to fall 6 m.
Given:
y₀ = 6 m
y = 0 m
v₀ = 0 m/s
a = -9.8 m/s²
Find: t
y = y₀ + v₀ t + ½ at²
(0 m) = (6 m) + (0 m/s) t + ½ (-9.8 m/s²) t²
t = 1.11 s
Now find the horizontal position of the target after that time:
Given:
x₀ = 6 m
v₀ = 5 m/s
a = 0 m/s²
t = 1.11 s
Find: x
x = x₀ + v₀ t + ½ at²
x = (6 m) + (5 m/s) (1.11 s) + ½ (0 m/s²) (1.11 s)²
x = 11.5 m
Finally, find the launch velocity needed to travel that distance in that time.
Given:
x₀ = 0 m
x = 11.5 m
t = 1.11 s
a = 0 m/s²
Find: v₀
(11.5 m) = (0 m) + v₀ (1.11 s) + ½ (0 m/s²) (1.11 s)²
v₀ = 10.4 m/s
