To determine when and at what height the two balls meet, we need to consider their respective motion equations and find the point of intersection.
Let's analyze the motion of each ball individually.
For the first ball: Initial velocity, u1 = 40 m/s (thrown upwards) Acceleration due to gravity, a = -9.8 m/s² (negative because it acts downwards)
For the second ball: Initial velocity, u2 = 60 m/s (thrown upwards) Acceleration due to gravity, a = -9.8 m/s²
Let's denote the time at which the two balls meet as t. At this time, both balls will have the same height.
Using the motion equation: h1 = u1 * t + (1/2) * a * t² (for the first ball) h2 = u2 * t + (1/2) * a * t² (for the second ball)
Since the heights are equal at the point of intersection, we can set h1 equal to h2:
u1 * t + (1/2) * a * t² = u2 * t + (1/2) * a * t²
Simplifying the equation: u1 * t = u2 * t 40 * t = 60 * t 20 * t = 0
We find that t = 0.
This implies that the two balls meet at the initial time when the second ball is thrown (t = 0 seconds). At this moment, they will have the same height.
To determine this height, we can substitute t = 0 into either of the motion equations:
h1 = u1 * t + (1/2) * a * t² h1 = 40 * 0 + (1/2) * (-9.8) * 0² h1 = 0
Therefore, at the moment the second ball is thrown (t = 0 seconds), the two balls meet at a height of 0 meters.