Answer:
0.014s
Step-by-step explanation:
Given parameters: 
Mass of the ball = 0.058kg 
Force = 260N 
Velocity of the ball = 63m/s 
Unknown: 
Time of contact = ? 
Solution: 
To solve this problem, we apply Newton's second law of motion which is mathematically expressed as; 
 Ft = m(v - u)
F is the force 
t is time 
m is the mass 
v is the final velocity 
u is the initial velocity = 0m/s
 Insert the parameters and find t; 
 260 x t = 0.058(63 - 0)
 260t = 3.65
 t = 0.014s