A package is dropped from a helicopter that is descending steadily at a speed v0. After t seconds have elapsed, consider the fol

The expected measurements should range as follows: 5, 10, 15, 20, and 25 meters.

Answer:

Explanation:

Provided:

The trolley, with mass M, is allowed to roll freely without friction.

The coefficient of friction between the trolley and mass m is .

A force F is applied to mass m.

The acceleration of the system is

The frictional force will counterbalance the weight of the block.

The frictional force is

If my calculations are accurate, the angle is 67.5 degrees.

Answer:

35.79 meters

Explanation:

We have an archer, and there is a target. Denote the distance between them as d.

The bowman releases the arrow, which travels the distance d at a velocity of 40 m/s until it hits the target. We establish the equation as:

Right after this, the arrow produces a muffled noise, traveling the same distance d at a speed of 340 m/s in time . Thus, we can derive:

.

Consequently, the sound reaches the archer, precisely 1 second post-firing the bow, resulting in:

.

Using this relationship in the distance formula for sound allows us to write:

.

Substituting the value of d from the first equation yields:

.

Now, after some calculations, we can proceed further:

.

Finally, the value is inserted into the initial equation:

<span>3.834 m/s. To solve this problem, we must ensure that the centripetal force equals or exceeds the gravitational force acting on the object. The formula for centripetal force is F = mv^2/r while the equation for gravitational force is F = ma. Since the mass (m) cancels out in both equations, we can equate them, leading to a = v^2/r. Now, inserting the given values (where the radius is half the diameter) allows us to find v: 9.8 m/s^2 <= v^2/1.5 m, which simplifies to 14.7 m^2/s^2 <= v^2. Therefore, we find that the minimum velocity required is 3.834057903 m/s <= v. Thus, the necessary speed is 3.834 m/s.</span>