Assume acceleration due to gravity=10 m/s. A ball is thrown vertically upward from top of a building with speed of 20 m/s. On the way back ball misses the building and lands on the ground. Total time the ball is in air is 6 seconds. Determine the height of the building with speed of 30 m/s.
To determine the height of the building, we can use the equation of motion for an object thrown vertically upward and downward. The equation is:
h = ut + (1/2)gt^2
where:
h = height of the building (the distance traveled by the ball)
u = initial velocity
g = acceleration due to gravity (which is given as 10 m/s^2)
t = time of flight
In this case, we know the following information:
Initial velocity when thrown upward, u = 20 m/s
Total time of flight, t = 6 seconds
1. First, let's find the time taken to reach the maximum height (when the ball is thrown upward and starts to fall back down). We can do this by using the equation for time:
t = u/g
Given u = 20 m/s and g = 10 m/s^2:
t = 20/10 = 2 seconds
2. We can now calculate the time taken for the ball to fall back down:
t_fall = total time of flight - time to reach maximum height
t_fall = 6 - 2 = 4 seconds
3. Using the equation of motion, we can calculate the maximum height reached by the ball:
h_max = ut - (1/2)gt^2
Given u = 20 m/s and t = 2 seconds, and g = 10 m/s^2:
h_max = (20 * 2) - (0.5 * 10 * (2)^2) = 40 - 20 = 20 meters
4. Now, to find the height of the building when the ball was thrown with a speed of 30 m/s, we know that the total time of flight is 6 seconds. So, we can calculate the time taken to fall from the maximum height:
t_fall_max = total time of flight - time to reach maximum height
t_fall_max = 6 - 2 = 4 seconds
5. Using the equation of motion, we can calculate the distance traveled during the fall:
h_fall_max = ut - (1/2)gt^2
Given u = 30 m/s and t = 4 seconds, and g = 10 m/s^2:
h_fall_max = (30 * 4) - (0.5 * 10 * (4)^2) = 120 - 80 = 40 meters
6. Finally, to find the height of the building, we need to find the total distance traveled by the ball. This can be done by summing up the distance traveled during the upward motion and the distance traveled during the downward motion:
Total distance = h_max + h_fall_max = 20 + 40 = 60 meters
Therefore, the height of the building when the ball was thrown with a speed of 30 m/s is 60 meters.