a ball thrown vertically from the ground level hits the ground after 4secs.calculatethe maximumheight it reachedduringit's journey.(g=10m/s2)
Gee! I wish I could take a class called "Better Days!"
well g is closer to 9.81 but I will play along.
I like to split this in two.
It will take two seconds to reach max height
at max height, v = 0
but
v = Vi - g t
so at the top
0 = Vi - 10 t or
Vi = 10 (2) = 20 m/s
h = Vi t - (g/2) t^2
h = 20 * 2 - 5(4)
= 20 meters
To calculate the maximum height reached by the ball, we need to use the formula for the vertical motion of an object:
h = (v₀² - v²) / (2g)
Where:
- h is the maximum height reached
- v₀ is the initial velocity of the ball
- v is the final velocity of the ball
- g is the acceleration due to gravity (10 m/s²)
In this case, the ball is thrown vertically upwards, so the initial velocity v₀ is positive and the final velocity v is negative (since it falls downwards).
First, let's find the initial velocity v₀ of the ball. We can use the time taken for the ball to hit the ground:
t = 4 seconds
The total time of flight is the time taken to reach the maximum height and then return to the ground. Since the ball is thrown vertically upwards, it will take the same amount of time to reach the maximum height and fall back down:
t_total = 4 seconds
Therefore, the time taken to reach the maximum height is half of the total time:
t_max_height = t_total / 2 = 4 seconds / 2 = 2 seconds
Now, we can use the time taken to reach the maximum height to calculate the initial velocity. We can use the following equation:
v = v₀ - gt_max_height
Since the final velocity v at the maximum height is zero (the ball momentarily stops before falling back down), we can rearrange the equation:
v₀ = gt_max_height
Substituting the given values:
v₀ = 10 m/s² * 2 s = 20 m/s
Now, we have the initial velocity v₀ of the ball. We can now use the formula to calculate the maximum height reached:
h = (v₀² - v²) / (2g)
Since the final velocity v is zero at the maximum height, the equation becomes:
h = v₀² / (2g)
Plugging in the values:
h = (20 m/s)² / (2 * 10 m/s²) = 400 m²/s² / 20 m/s² = 20 meters
Therefore, the maximum height reached by the ball during its journey is 20 meters.