<span>When the fuel of the rocket is consumed, the acceleration would be zero. However, at this phase the rocket would still be going up until all the forces of gravity would dominate and change the direction of the rocket. We need to calculate two distances, one from the ground until the point where the fuel is consumed and from that point to the point where the gravity would change the direction.
Given:
a = 86 m/s^2
t = 1.7 s
Solution:
d = vi (t) + 0.5 (a) (t^2)
d = (0) (1.7) + 0.5 (86) (1.7)^2
d = 124.27 m
vf = vi + at
vf = 0 + 86 (1.7)
vf = 146.2 m/s (velocity when the fuel is consumed completely)
Then, we calculate the time it takes until it reaches the maximum height.
vf = vi + at
0 = 146.2 + (-9.8) (t)
t = 14.92 s
Then, the second distance
d= vi (t) + 0.5 (a) (t^2)
d = 146.2 (14.92) + 0.5 (-9.8) (14.92^2)
d = 1090.53 m
Then, we determine the maximum altitude:
d1 + d2 = 124.27 m + 1090.53 m = 1214.8 m</span>
Answer:
The tension increases to four times its original value.
Explanation:
v = Velocity
r = Radius
m = Mass of stone
The centripetal force is

The tension will balance the centripetal force



The new tension will be 4 times the old tension
Answer:
(a)
P₂ = 7.13 atm
(b)
T₂ = 157.14 K
Explanation:
(a)
V₁ = initial volume = 3.7 L = 3.7 x 10⁻³ m³
V₂ = final volume = 0.85 L = 0.85 x 10⁻³ m³
P₁ = Initial Pressure of the gas = 0.91 atm = 0.91 x 101325 = 92205.75 Pa
P₂ = Final Pressure of the gas = ?
Using the equation


= 722860 Pa
= 7.13 atm
(b)
T₁ = initial temperature =283 K
T₂ = Final temperature = ?
using the equation


T₂ = 157.14 K
So we wan't to know what is the velocity after a collision of two railroad cars, one moving to the east and the other moving to the west if m1=2000kg, v1=5m/s and m2=6000kg, v2=3m/s. We can find the solution using the law of conservation of momentum for plastic collisions that states that the momentum must remain constant before (left side of the equation) and after (right side of the equation) the collision: m1*v1+m2*v2=(m1+m2)*v. So now we simply plug in the numbers and get: 2000kg * 5m/s + 6000kg * 3m/s = (2000kg + 6000kg)*v. Now we can write: 10000 kgm/s + 18000 kgm/s = 8000kg * v. To get v, the velocity of both railroad cars after the collision we simply divide both sides of the equation with 8000 kg: so v=3.5m/s to the west.
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