A ball is thrown vertically upward with a speed of 1.86 m/s from a point 3.82 m above the ground.Calculate the time in which the ball will reach the ground.

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lemjay | High School Teacher | (Level 3) Senior Educator

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To solve for t, use the formula:

`s=v_it + 1/2at^2`

where `s`   - displacement          `v_i` - initial velocity 

          `t`   - time                       `a`   - accelaration

Note that displacement refers to the change in height. So value of s is:


Also, acceleration is equal to gravity since the ball exhibits the principle of freely falling bodies. Its sign is negative because the direction of the intial velocity is upward. So, `a=-9.81 m/s^2` .

Then, substitute `s=-3.82` , `v_i=1.86` and `a=-9.82` .

`-3.82=1.86t + 1/2(-9.82)t^2`


Express the equation in quadratic form `ax^2+bx+c=0` .


Apply the quadratic formula to solve for t.



`t_1=1.09`       and      `t_2= -0.71`

Since t represents time, take only the positve value.

Hence, the time it takes for the ball to reach the ground is 1.09 seconds.

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