Answer:
The second tennis ball will arrive at the ground 3.26 seconds after the first tennis ball lands.
Step-by-step explanation:
Let's start by finding the time it takes for the first tennis ball to reach the ground. We can use the formula:
h = 1/2 gt^2 + v0t + h0
where:
h = height (in this case, 42 meters, since the ball is thrown from the top of the building)
g = acceleration due to gravity (9.8 m/s^2)
v0 = initial velocity (in this case, -16 m/s, since the ball is thrown downward)
h0 = initial height (in this case, 0 meters)
We want to solve for t, the time it takes for the first ball to hit the ground. We can rearrange the equation to solve for t:
t = sqrt(2h/g)
t = sqrt(2 x 42/9.8) = 3.23 seconds (rounded to two decimal places)
So the first tennis ball takes 3.23 seconds to hit the ground. Now we can use this time to find out when the second tennis ball will arrive at the ground.
The second tennis ball is thrown upward with an initial velocity of 16 m/s, and we know that it will eventually hit the ground with a final velocity of -16 m/s (the same speed as the first ball). We can use the formula:
v = v0 + gt
to find out how long it takes for the second ball to reach a velocity of 0 m/s (when it reaches the highest point of its trajectory) and then use this time to calculate the total time it takes for the ball to hit the ground.
At the highest point of its trajectory, the second ball has a velocity of 0 m/s. We can use the formula to solve for the time it takes to reach this point:
0 = 16 - 9.8t
t = 16/9.8 = 1.63 seconds (rounded to two decimal places)
It takes 1.63 seconds for the second ball to reach the highest point of its trajectory. From this point, it will take the same amount of time to reach the ground as it took for it to reach the highest point, so the total time it takes for the second ball to hit the ground is:
t = 1.63 + 1.63 = 3.26 seconds (rounded to two decimal places)