Question

A ball is thrown upward at 189 m/s from a height of 20 meters off the ground. How long will it take for the ball to be at ground level?

Answer 1

To determine the time it takes for the ball to reach ground level, we can use the equations of motion. The key equation to use in this scenario is:

$s=ut+\frac{1}{2}a{t}^2$,

where:

• $s$ is the displacement (change in position),
• $u$ is the initial velocity,
• $t$ is the time, and
• $a$ is the acceleration.

In this case, the initial velocity of the ball is $u=189\text{m/s}$ (upward), the initial displacement is $s=-20\text{m}$ (negative because the ball is above the ground), and the acceleration is $a=-9.8{\text{m/s}}^2$ (due to gravity, downward).

Plugging in these values into the equation, we have:

$-20=189t+\frac{1}{2}(-9.8)t^2$.

Rearranging the equation to bring all terms to one side, we get:

−4.9t2+189t−20=0-4.9t^2 + 189t - 20 = 0−4.9t2+<span class="m