Answer:
14.85 m/s
Explanation:
From the question given above, the following data were obtained:
Height (h) of tower = 45 m
Horizontal distance (s) moved by the balloon = 45 m
Horizontal velocity (u) =?
Next, we shall determine the time taken for the balloon to hit the shoe of the passerby. This is illustrated below:
Height (h) of tower = 45 m
Acceleration due to gravity (g) = 9.8 m/s²
Time (t) =?
h = ½gt²
45 = ½ × 9.8 × t²
45 = 4.8 × t²
Divide both side by 4.9
t² = 45/4.9
Take the square root of both side
t = √(45/4.9)
t = 3.03 s
Finally, we shall determine the magnitude of the horizontal velocity of the balloon as shown below:
Horizontal distance (s) moved by the balloon = 45 m
Time (t) = 3.03 s
Horizontal velocity (u) =?
s = ut
45 = u × 3.03
Divide both side by 3.03
u = 45/3.03
u = 14.85 m/s
Thus, the magnitude of the horizontal velocity of the balloon was 14.85 m/s
Answer: v = 2.24 m/s
Explanation: The <u>Law</u> <u>of</u> <u>Conservation</u> <u>of</u> <u>Energy</u> states that total energy is constant in any process and, it cannot be created nor destroyed, only transformed.
So, in the toy launcher, the energy of the compressed spring, called <u>Elastic</u> <u>Potential</u> <u>Energy (PE)</u>, transforms into the movement of the plastic sphere, called <u>Kinetic</u> <u>Energy (KE)</u>. Since total energy must be constant:

where the terms with subscript i are related to the initial of the process and the terms with subscript f relates to the final process.
The equation is calculated as:






v = 2.24
The maximum speed the plastic sphere will be launched is 2.24 m/s.
Answer:
<em>The final speed of the second package is twice as much as the final speed of the first package.</em>
Explanation:
<u>Free Fall Motion</u>
If an object is dropped in the air, it starts a vertical movement with an acceleration equal to g=9.8 m/s^2. The speed of the object after a time t is:

And the distance traveled downwards is:

If we know the height at which the object was dropped, we can calculate the time it takes to reach the ground by solving the last equation for t:

Replacing into the first equation:

Rationalizing:

Let's call v1 the final speed of the package dropped from a height H. Thus:

Let v2 be the final speed of the package dropped from a height 4H. Thus:

Taking out the square root of 4:

Dividing v2/v1 we can compare the final speeds:

Simplifying:

The final speed of the second package is twice as much as the final speed of the first package.
Gay Lussac's Law states: At a constant volume Pressure<span> divided by </span>Temperature<span> is</span>constant<span> P/T = k Together these three laws form the foundation of the Ideal </span>Gas<span>Law. Objective: Students will </span>investigate<span> Gay Lussac's Law relating </span>pressure<span> and</span>temperature<span> at a </span><span>constant temperature.</span>
Average speed = (total distance covered) / (time to cover the distance)
Total distance = (80m) + (125m) + (45m) = 250 meters
Overall time = 10 minutes
Average speed = (250 meters) / (10 minutes)
<em>Average speed = 25 meters/minute </em>
Since we're only looking for average speed and not velocity, we don't care about any of the directions, and we don't need to calculate Mary's displacement.