Consider an event with space-time coordinates (t=2.00s, x=2.50×108m) in an inertial frame of reference s. let s' be a second inertial frame of reference moving, in the positive x direction, with speed 2.70×108m/s relative to frame s. find the value of γ that will be needed to transform coordinates between frames s and s'. use c=3.00×108m/s for the speed of light in vacuum.

The value of γ needed for transformation between the two frames is 2.2942.

To transform the position, time, mass from one coordinate frame to another frame which moves with a speed v relative to the first, we need to calculate the Lorentz constant γ .

This is given by,

Substitute for v and for c.

The Lorentz factor needed for transforming the position and time coordinates from the given frame to the frame moving with a speed v relative to it is 2.2942

here we know that ball will drop down by total distance 3.2 m

so here we know that

now using kinematics

now in the same time it will cover horizontal distance of 0.75 m

so speed of the ball will be