Question 427.
A Rubber ball is dropped from a height of 27m.; Each time that it hits the ground it bounces to a height 2/3 of that from which it fell. Find the total distance travelled by the ball until it comes to rest?
Answer 427.
Total distance = 27 + (2/3) * 27 + (2/3) * 27 + (2/3)^2 * 27 + (2/3)^2 * 27 + ...
= 27 [1 + 2*(2/3) + 2 * (2/3)^2 + ...]
= 27 [1 + 2*(2/3) {1 + (2/3) + (2/3)^2 + ...}]
= 27 [1 + 2*(2/3) * 1/(1 - 2/3)]
= 27 [1 + 4/3 * (3/1)]
= 135 m.
Link to YA!
A Rubber ball is dropped from a height of 27m.; Each time that it hits the ground it bounces to a height 2/3 of that from which it fell. Find the total distance travelled by the ball until it comes to rest?
Answer 427.
Total distance = 27 + (2/3) * 27 + (2/3) * 27 + (2/3)^2 * 27 + (2/3)^2 * 27 + ...
= 27 [1 + 2*(2/3) + 2 * (2/3)^2 + ...]
= 27 [1 + 2*(2/3) {1 + (2/3) + (2/3)^2 + ...}]
= 27 [1 + 2*(2/3) * 1/(1 - 2/3)]
= 27 [1 + 4/3 * (3/1)]
= 135 m.
Link to YA!
No comments:
Post a Comment