Mary throws a ball from her balcony downwards as it is shown in the figure. How long does it take to reach the ground? What is the balcony height?
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i do not know
To determine how long it takes for the ball to reach the ground and the height of the balcony, we need to consider the motion of the ball using the principles of physics.
Firstly, we need to know the acceleration due to gravity, which is approximately 9.8 meters per second squared (m/s^2) on Earth.
Next, we can use the kinematic equation for vertical motion:
s = ut + (1/2)gt^2
Where:
s = distance traveled
u = initial velocity (in this case, 0 m/s since the ball is thrown downwards)
g = acceleration due to gravity
t = time taken
In this scenario, the initial velocity is 0 m/s because the ball is thrown downwards with no initial upward velocity.
Now let's break down the problem step by step:
1) Finding the time it takes for the ball to reach the ground:
Since we know the initial velocity (u) is 0 m/s and the ball is dropped from rest, we can simplify the kinematic equation to:
s = (1/2)gt^2
Where s is the height of the balcony, and t is the time taken to reach the ground.
Given that we want to find the time (t) and the height (s), we need to rearrange the equation:
t = sqrt(2s/g)
2) Finding the height of the balcony:
Since we have the time (t) it takes for the ball to reach the ground, we can use the same kinematic equation to find the height (s) of the balcony:
s = (1/2)gt^2
We substitute the value of t we obtained in step 1 to find the height (s).
By following these steps and applying the appropriate equations, you can find both the time it takes for the ball to reach the ground and the height of the balcony