To answer question 1, we can use the equations of motion, specifically the one relating distance, time, initial velocity, and acceleration. In this case, the initial velocity is the velocity with which the ball is thrown upward, and the distance is the total vertical distance covered by the ball (233 m).
First, we need to find the time taken for the ball to go up to the highest point (where its velocity becomes zero) and then come back down to the ground. Since the acceleration due to gravity is acting in the opposite direction during the upward motion, we can use the equation:
v = u + at
Where:
v is the final velocity (zero in this case as the ball reaches its highest point),
u is the initial velocity (the upward velocity with which the ball is thrown),
a is the acceleration due to gravity (-9.8 m/s^2),
and t is the time taken.
Rearranging the equation to solve for time (t), we get:
t = (v - u) / a
Substituting the given values, v = 0 m/s, u = initial upward velocity, and a = -9.8 m/s^2, we can solve for time.
Now to calculate the time taken for the ball to go up and come back down, we need to find the time taken for the upward motion and multiply it by 2, as the downward motion will take the same amount of time. Once we have the time, we can specify the answer in units of seconds.
To answer question II, we can apply the concept of relative motion. We need to find the point where the two objects meet, which means both objects will have covered the same distance vertically.
First, we need to find the time it takes for the first object to reach the ground. We can use the equation of motion:
v^2 = u^2 + 2as
Where:
v is the final velocity (which is 0 m/s when the object reaches the ground),
u is the initial velocity (given as 17 m/s),
a is the acceleration due to gravity (9.8 m/s^2),
and s is the distance traveled (which is the initial height of 96 m).
Rearranging the equation to solve for time (t), we get:
t = (v - u) / a
Substituting the given values, v = 0 m/s, u = 17 m/s, and a = 9.8 m/s^2, we can solve for time.
Next, we need to find the time it takes for the second object to reach the point of intersection. We can use the same equation of motion:
t = (v - u) / a
Substituting the given values, v = 0 m/s (as the object reaches the highest point where velocity becomes zero), u = 22 m/s, and a = -9.8 m/s^2, we can solve for time.
Since the two objects are moving towards each other and have started at different heights, we can calculate the distance covered by each object using the formula:
s = ut + (1/2)at^2
Where:
s is the distance covered,
u is the initial velocity,
t is the time taken,
and a is the acceleration.
By calculating the distance covered by each object at the time of intersection, we can determine the height above the ground where the objects meet.