Dee is on a swing in the playground. the chains are 2.5 m long, and the tension in each chain is 450 n when dee is 55 cm above t

Answer:

The plane's speed in relation to the ground is 300.79 km/h.

Explanation:

Provided details include:

Wind speed = 75.0 km/hr

Plane's airspeed = 310 km/hr

Next, we must find the ground speed of the plane

Calculating the angle

Using the angle formula

Where v' represents the wind speed

v represents the plane's speed

We will substitute the values into the formula

Now, we must find the resultant speed

Using the resultant speed formula

Insert the values into the formula

Consequently, the plane's speed in relation to the ground equals 300.79 km/h.

Answer:

The duration, t = 3.53 seconds

Explanation:

The following information is provided:

The equation to calculate the time t is expressed as:

...... (1)

Where

s denotes the distance in feet

We are to determine the duration taken by the stone to fall a distance of 200 feet, where s = 200 feet

Substituting the value of s into equation (1) yields:

t = 3.53 seconds

Thus, the time taken by the object is 3.53 seconds, which provides the required answer.

Answer:

The ratio of mass that is discarded is determined by this equation:

M - m = (3a/2)/(g²- (a²/2) - (ag/2))

Explanation:

The force acting on an object in motion is defined by the equation:

F = ma

Additionally, there is a gravitational force consistently acting downwards on the object, defined as g = 9.8 ms⁻²

For convenience, we will utilize a positive notation for downward acceleration and a negative notation for upward acceleration.

Case 1:

The hot air balloon has mass = M

Acceleration = a

Upward thrust from hot air = F = constant

Gravitational force acting downward = Mg

The net force on the balloon can be expressed as:

Ma = Gravitational force - Upward Force                              

Ma = Mg - F                      (since the balloon moves downward, that means Mg > F)

F = Mg - Ma

F = M (g-a)

M = F/(g-a)

Case 2:

After releasing the ballast, the new mass becomes m. The new upward acceleration is -a/2:

The net force is expressed as:

-m(a/2) = mg - F        (The balloon is moving upwards, hence F > mg)

F = mg + m(a/2)

F = m(g + (a/2))

m = F/(g + (a/2))

Determining the fraction of the mass initially dropped: