To determine when the ball will reach the ground, we can use the equations of motion and consider the vertical motion of the ball.
Given: Initial velocity (u) = 100 m/s (upwards) Final velocity (v) = ? Acceleration (a) = -9.8 m/s² (assuming gravitational acceleration, considering downward direction) Displacement (s) = ?
The equation to calculate the displacement of an object under constant acceleration is:
s = ut + (1/2) * a * t²
Since the ball reaches the ground, its final displacement (s) is zero. We need to solve for the time (t) it takes for the ball to reach the ground.
0 = (100) * t + (1/2) * (-9.8) * t²
Rearranging the equation, we get:
-4.9t² + 100t = 0
Factoring out t, we have:
t * (-4.9t + 100) = 0
This equation gives two possible solutions: t = 0 or -4.9t + 100 = 0.
Since we're interested in the time it takes for the ball to reach the ground, we discard the t = 0 solution (which corresponds to the initial time).
Now, solve the equation -4.9t + 100 = 0 for t:
-4.9t + 100 = 0 4.9t = 100 t = 100 / 4.9 t ≈ 20.41 seconds
Therefore, the ball will reach the ground after approximately 20.41 seconds.