Answer:
(a) The two balls collide after launch.
(b) The height of the collision is .
(Assuming that air resistance is negligible.)
Explanation:
Let vector quantities (displacements, velocities, acceleration, etc.) that point upward be positive. Conversely, let vector quantities that point downward be negative.
The gravitational acceleration of the earth points dowards (towards the ground.) Therefore, the sign of should be negative. The question states that the magnitude of
is
. Hence, the signed value of
should be
.
Similarly, the initial velocity of the ball thrown downwards should also be negative: .
On the other hand, the initial velocity of the ball thrown upwards should be positive: .
Let and
denote the initial velocity and height of one such ball. The following SUVAT equation gives the height of that ball at time
:
.
For both balls, .
For the ball thrown downwards:
- Initial velocity:
.
- Initial height:
.
(where
is in meters and
is in seconds.)
Similarly, for the ball thrown upwards:
- Initial velocity:
.
- Initial height:
.
(where
is in meters and
is in seconds.)
Equate the two expressions and solve for :
.
.
Therefore, the collision takes place after launch.
Substitute into either of the two original expressions to find the height of collision:
.
In other words, the two balls collide when their height was .