Question

1.Give an example where the velocity of an object is zero but its acceleration is not zero? 2.A ball A is dropped from the top of a building and at the same time an identical ball B is thrown vertically upward from the ground. When the balls collide the speed of A is twice that of B. At what fraction of the height of the building did the collision occur?

Answer 1

Explanation:

Let height of building is h and x is the desired fraction.

for ball A,

initial velocity of ball A , u = 0

distance covered by ball A = (1 - x)h

so, use formula, S = ut + 1/2at²

(1 - x)h = 0 + 1/2 × g × t²

(1 - x)h = gt²/2

t = √{2(1 - x)h/g}

velocity at t sec , v = u + at

v = 0 + g√{2(1 - x)h/g} = √{2g(1 - x)h}......(1)

for ball B,

distance covered by ball B , S = xh

use formula, S = ut + 1/2at²

xh = u√{2(1-x)h/g} - 1/2 × g × (√{2(1-x)h/g})²

after solving , we get, u = √{gh/2(1 - x)}

velocity at t sec., v = u + at

= √{gh/2(1 - x)} -g√{2(1 -x)h/g}

= √{gh/2(1 - x)} - √{2g(1 - x)h} .......(2)

A/C to question,

√{2g(1-x)h} =2[√{gh/2(1 - x)} - √{2g(1 - x)h} ]

3√{2g(1 - x)h} = 2√{gh/2(1 - x)}

9(1 - x) = 1/(1 - x)

9(1 - x)² = 1

x = 2/3.