A ball falls from a height

BallIntheAirA ball falls from a height h = 100 m. Please find the average speed of its movement in the second half of the way. The initial velocity of the ball is zero and the gravitational acceleration is g = 9.8 m/s^2. The ball may be regarded as a point particle and air resistance neglected.

Solution. Posted on Wednesday, April 15, 2015.

We will use the following formula
Yf=Yi+Vi*t-g*t^2/2, where Yf – the final position of the ball, Yi – the initial position of the ball, Vi – the initial velocity, g – gravitational acceleration (9.8 m/s^2) and t – the time which the ball needs to move from the initial position to the final position.

Yf = 0, Yi = h, Vi = 0

So, an equation of time will be

Now, let’s find an equation of time t1 for the first half of the way

from this,

The time of the second half of the way will be

Finally, the average speed will be

V=0.5*100/[(√2−1)*√(100/9.8)] = 37.79 m/s


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