To find the time and height at which the two balls meet, we need to consider their individual motions and determine the point of intersection.
Let's analyze the motion of each ball separately:
For the first ball: Initial velocity (u1) = 40 m/s Acceleration due to gravity (a) = -9.8 m/s^2 (taking downwards as negative)
Using the equation of motion: s1 = u1t + (1/2)at^2, where s1 is the displacement of the first ball at time t, we can calculate the height of the first ball after 1.0 second:
s1 = (40 m/s)(1.0 s) + (1/2)(-9.8 m/s^2)(1.0 s)^2 s1 = 40 m - 4.9 m s1 = 35.1 m
Now, let's consider the motion of the second ball: Initial velocity (u2) = 60 m/s Acceleration due to gravity (a) = -9.8 m/s^2
Using the same equation of motion, we can calculate the height of the second ball at time t:
s2 = (60 m/s)t + (1/2)(-9.8 m/s^2)t^2
For the balls to meet, their heights (s1 and s2) must be equal at a certain time (t). Therefore, we set s1 equal to s2 and solve for t:
35.1 m = (60 m/s)t + (1/2)(-9.8 m/s^2)t^2
This equation is a quadratic equation in t. By solving this equation, we can find the value of t when the two balls meet.
Unfortunately, the quadratic equation cannot be solved explicitly for t in terms of a simple formula. We can solve it numerically or using numerical methods such as approximation techniques or graphing tools.
So, the exact time and height at which the two balls meet cannot be determined without additional information or using numerical methods.