Question

An athlete performing a long jump leaves the ground at a 33.3 degrees angle and lands 7.75 m away. What was the takeoff speed? If this speed were increased by just 5.0%, how much longer would the jump be?

Answer 1

Angle of inclination of athlete with the horizontal is

Distance covered by long jump is

Initial take off speed is

Using kinematics equation    in horizontal direction, (since )

Where is the time taken to cover the distance.

In the time , the athlete covers a total vertical distance ( starts from ground and reaches ground )

Using kinematics equation   in vertical direction  

( since )

Horizontal distance covered is

Athlete's takeoof speed is

If the speed is increased by 5.0% ,

The athlete lands away.

Difference in lengths is

He can jump longer than his previous jump.