Answer :
Final answer:
The time it takes for the ball to reach the ground can be calculated using the equation of motion. Given the initial velocity, acceleration due to gravity, and distance, we solve for time. The positive root of the resulting quadratic equation gives us the time of 2.6 seconds.
Explanation:
In this case, we use the equation of linear motion. Initial velocity (u) for the ball is given as 10 m/s downward, acceleration (a) due to gravity is 9.8 m/s^2 downward, and the distance (d) is 38.4 m. Here's the equation:
d=ut+(1/2)at^2
If we plug in the values:
38.4 = (10*t) + 0.5 * 9.8 * t^2
This is a quadratic equation in the form of at^2+bt+c=0, where a=0.5 * 9.8, b=-10 and c=-38.4. Solving this equation will give you the time (t) which represents how long the ball takes to reach the ground. The positive root of this equation is 2.6 seconds.
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