Centripetal acceleration is given by the formula
Since we know the value of the acceleration is 9.8 m/s² and we know r, we can solve for the speed, which is the magnitude of v. Note the value of a is just the acceleration due to gravity, which is what makes the rocket orbit and not fly off into space.
When the iron and the water reach thermal equilibrium, they have same temperature,
.
We can consider this as an isolated system, so the heat released by the water is equal to the heat absorbed by the iron.
The hear released by the water is:
where
is the water mass,
is the specific heat of the water, and
is the variation of temperature of the water.
Similarly, the heat absorbed by the iron is:
where
is the iron mass,
is the iron specific heat, and
is the variation of temperature of the iron.
Writing
and replacing the numbers, we can solve to find mw, the mass of the water:
Answer:
u/2 √(1 + 3 cos² θ)
Explanation:
The object is thrown at an angle θ, so the velocity has two components, vertical and horizontal.
Initially, the vertical component is u sin θ and the horizontal component is u cos θ.
At the maximum height, the vertical component is 0 and the horizontal component is u cos θ.
The mean vertical velocity is:
(u sin θ + 0) / 2 = u/2 sin θ
The mean horizontal velocity is:
(u cos θ + u cos θ) / 2 = u cos θ
The net mean velocity can be found with Pythagorean theorem:
v² = (u/2 sin θ)² + (u cos θ)²
v² = u²/4 sin² θ + u² cos² θ
v² = u²/4 (1 − cos² θ) + u² cos² θ
v² = u²/4 (1 − cos² θ) + u²/4 (4 cos² θ)
v² = u²/4 (1 − cos² θ + 4 cos² θ)
v² = u²/4 (1 + 3 cos² θ)
v = u/2 √(1 + 3 cos² θ)
Answer:
Explanation:
When we do multiple trials of the same experiment, we can make sure that our results are consistent and not altered by random events. Multiple trials can be done at one time. If we were testing a new fertilizer, we could test it on lots of individual plants at the same time.
Answer:
-3802 m/s
Explanation:
The y-component of the final velocity is ...
(6598 m/s)·sin(-20.5°) ≈ -2310.7 m/s
The y-component of the velocity due to acceleration is ...
(5200 m/s²)(0.350 s)sin(55°) ≈ 1490.9 m/s
Then the initial velocity in the y-direction is found from ...
initial velocity + change in velocity = final velocity
initial velocity = (final velocity) - (change in velocity)
= -2310.7 m/s - 1490.9 m/s ≈ -3802 m/s
