Physics

To find the initial velocity required for a basketball launched at an angle of 75° to land exactly 10 meters horizontally away, we can use the following steps.

 

Given Data

Horizontal Distance (): 10 meters

Launch Angle (): 75°

Acceleration due to Gravity (): 10 m/s²

 

Set Up the Horizontal Motion Equation

The horizontal distance can be calculated using the equation:

Where is the horizontal component of the initial velocity, which can be expressed as:

 

Calculate Time of Flight

To find the time of flight, we can express it in terms of the initial velocity:

 

Set Up the Vertical Motion Equation

For vertical motion, we use:

Since we want the ball to land back at the same vertical level (ground level), we set :

Where .

 

 

This simplifies to: