A basketball leaves a player's hands at a height of 2.20 m above the floor. The basket is 2.70 m above the floor. The player likes to shoot the ball at a 36.0 ∘ angle. Of the shot is made from a horizontal distance of 9.10 m and must be accurate to ±0.23m (horizontally), what is the range of initial speeds allowed to make the basket

The range of initial speeds allowed to make the basket is: .

Explanation:

We must notice that basketball depicts a parabolic motion, which consists of combining a constant speed motion in x-direction and free fall motion in the y-direction. The motion is described by the following kinematic formulas:

x-Direction

y-Direction

Where:

, - Initial position of the basketball, measured in meters.

, - Final position of the basketball, measured in meters.

- Initial speed of the basketball, measured in meters per second.

- Time, measured in seconds.

- Tilt angle, measured in sexagesimal degrees.

- Gravitational acceleration, measured in meters per square second.

If we know that , , , , and , the system of equation is reduce to this:

(Ec. 1)

(Ec. 2)

At first we clear in (Ec. 1):

(Ec. 1) in (Ec. 2):

Now we clear the time in the resulting expression:

There are two solutions:

The initial velocity is cleared within (Ec. 2):

The bounds of the range of initial speed is determined hereafter:

The range of initial speeds allowed to make the basket is: .

when two balls of the different masses are dropped from equal height, they reach the ground at the same time .this is because they experience the same acceleration.

the acceleration is independent of mass.

thus when they are dropped they will always maintain the same velocity and travel the same distance (neglect air resistance of course) at the same time.

weight of the box is given as

here this is placed on the inclined of angle 42 degree

now this weight will have two components one is along the incline other is perpendicular to it

so here we need to apply a force parallel to incline opposite to its component of weight

so here the component of weight is given as

here we have

so it requires 75 n force to move it upwards