If such a particle is moving, with respect to the laboratory, with a speed of 0.950 c , what average lifetime is measured in the laboratory?

Complete Question

The positive , an unstable particle, lives on average  (measured in its own frame of reference) before decaying.

If such a particle is moving, with respect to the laboratory, with a speed of 0.950 c , what average lifetime is measured in the laboratory?

The value is  

Explanation:

From the question we are told that

   The the average live time of   is  

    The speed of of  in the laboratory is  

Generally the average life time of the positive measured in the laboratory  is mathematically represented as

initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft