Question

A plastic ball is dropped from a height of $1m$ and rebounds several times from the floor. If $0.13$ sec elapse from the moment it is dropped to the second impact with the floor, what is the coefficient of restitution?

• A. $0.85$
• B. $0.25$
• C. $0.39$
• D. $0.65$

Answer 1

The correct option is C $0.39$

Formulae,

velocity with which the ball strikes the floor for the first time

$v_1=\sqrt{2gh}=\sqrt{2\times 9.8\times 1}=4.472m/s$

time taken by the ball to strike the floor for the first time

$t_1=\frac{v_1}{g}=\frac{4.472}{9.8}=0.452s$

time taken by ball between first and second impact with the floor is

$t_2=1.3-t_1=1.3-0.452=0.848s$

time taken by ball for upward journey $=\frac{1}{2}{t}_2=\frac{1}{2}\times 0.848=0.424s$

upward velocity after first attempt $v_2=g\times \frac{1}{2}{t}_2=9.8\times 0.424=4.155m/s$

coefficient of restitution $=\frac{v_2}{v_1}=\frac{4.155}{4.472}=0.939$