Question

From 100m high tower a ball is dropped and other ball is thrown vertically upward with the velocity of 50m per sec.
1:After what time the two balls will cross each other?
2:Calculate the time for both balls to hit the ground?

Answer 1

Answer on Question #68696 Physics / Mechanics / Relativity

From 100m high tower a ball is dropped and other ball is thrown vertically upward with the velocity of 50m per sec.

1: After what time the two balls will cross each other?

2: Calculate the time for both balls to hit the ground?

Solution:

1) The law of motion for the balls are

$$x _ {1} = h - \frac {g t ^ {2}}{2}$$ $$x _ {2} = v _ {\text {initial}} t - \frac {g t ^ {2}}{2}$$

When two balls will cross each other

$$x _ {1} = x _ {2}$$

So

$$h - \frac {g t ^ {2}}{2} = v _ {\text {initial}} t - \frac {g t ^ {2}}{2}$$ $$t = \frac {h}{v _ {\text {initial}}} = \frac {100}{50} = 2 \text{ s.}$$

2) When ball to hit the ground

$$x _ {1} = 0 \text{ and } x _ {2} = 0.$$

Thus

$$t _ {1} = \sqrt {\frac {2 h}{g}} = \sqrt {\frac {2 \times 100}{9.8}} = 4.5 \text{ s}$$ $$t _ {2} = \frac {2 v _ {\text {initial}}}{g} = \frac {2 \times 50}{9.8} = 10.2 \text{ s}$$

Answers:

(1) 2 s;

(2) 4.5 s, 10.2 s.

Answer provided by www.AssignmentExpert.com