Answer:
Time, t = 5.355 seconds
Explanation:
Given the following data;
Distance = 100 m
Initial velocity = 16 m/s
Deceleration = 1 m/s²
To find the time, we would use the second equation of motion;
But since the ball is decelerating, it's acceleration would be negative.
S = ut + ½at²
Where;
S represents the displacement or height measured in meters.
u represents the initial velocity measured in meters per seconds.
t represents the time measured in seconds.
a represents acceleration measured in meters per seconds square.
Substituting into the equation, we have;
100 = 16t - 0.5t²
200 = 32t - t²
t² + 32t - 200 = 0
Solving the quadratic equation using the quadratic formula;
The quadratic equation formula is;
[tex] x = \frac {-b \; \pm \sqrt {b^{2} - 4ac}}{2a} [/tex]
Substituting into the equation, we have;
[tex] x = \frac {-32 \; \pm \sqrt {32^{2} - 4*1*(-200)}}{2*1} [/tex]
[tex] x = \frac {-32\pm \sqrt {1024 - (-800)}}{2} [/tex]
[tex] x = \frac {-32 \pm \sqrt {1024 + 800}}{2} [/tex]
[tex] x = \frac {-32 \pm \sqrt {1824}}{2} [/tex]
[tex] x = \frac {-32 \pm 42.71}{2} [/tex]
[tex] x_{1} = \frac {-32 + 42.71}{2} [/tex]
[tex] x_{1} = \frac {10.71}{2} [/tex]
x1 = 5.355
We do not need the negative value of x, so we proceed.
Therefore, time = 5.355 seconds
