A basketball center holds a basketball straight out, 2.0 m above the floor, and releases it. It bounces off the floor and rises

Answer:

a)

b)

c)

Explanation:

According to the problem, the distance from the building where the ball hits is 16m, and its final elevation exceeds the initial height by 8m.

With this information, we can compute the ball’s starting speed.

a) Let's first assess the horizontal trajectory.

(1)

This gives us our initial equation.

Next, we need to examine the vertical trajectory.

Utilizing in our first equation (1)

Now let’s solve for t.

The ball takes two seconds to reach the adjacent building, allowing us to compute its initial speed.

b) To determine the velocity magnitude just before impact, we must calculate both x and y components.

The computed velocity magnitude is:

c) The ball's angle is:

Answer:

All three pendulums will have the same angular frequencies.

Explanation:

For a simple pendulum, the time period using the approximation is expressed as:

The angular frequency is defined as

Since the angular frequency remains unaffected by the initial angle (valid strictly for small angle approximations), we deduce that the angular frequencies of the three pendulums are identical.

Answer:

Explanation:

The beacon is rotating at an angular speed of

so we have

We know that

At this point we have

So we can conclude with

Answer:

The average distance of the new asteroid from the Sun is estimated to be (2.02 × 10⁶) km.

Explanation:

The orbital speed of planets varies based on their distance from the Sun, which also affects their orbital period.

With its 557 months, equivalent to 46.4 years for an orbit around the Sun, the new asteroid's speed is situated between the orbital speeds of Saturn and Uranus.

Uranus orbits the Sun in 84 years at 24.61 km/hour,

while Saturn completes its orbit in 29.4 years at 34.82 km/hour.

To interpolate the speed for our asteroid at 46.4 years,

we denote its speed as x.

84 years ----> 24.61 km/h

46.4 years ----> x km/h

29.4 years -----> 34.82 km/h

Setting up the proportion:

(84 - 46.4)/(46.4 - 29.4) = (24.61 - x)/(x - 34.82)

Solving for x gives the asteroid's speed as 31.64 km/hr.

To find the average speed, use the formula:

Average speed = (total distance)/(time taken).

The total distance covered equals the circumference of the orbit around the Sun = 2πR,

where R = distance from the asteroid to the Sun.

Time taken = 16700 days = 16700 × 24 hours = 400800 hours.

Thus, we find that 31.64 = (2πR)/400800.

From this, we get 2πR = 31.64 × 400800 = 12681312 km.

And, R = 12681312/(2π) = 2018293.5 km = (2.02 × 10⁶) km.