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 find the time it takes for the ball to reach ground level, we can use the kinematic equation:

$h=h_0+v_{0}t-\frac{1}{2}g{t}^2$

where:

• $h$ is the final height (ground level) which is 0 in this case,
• $h_0$ is the initial height which is 20 meters,
• $v_0$ is the initial velocity which is 189 m/s,
• $g$ is the acceleration due to gravity, approximately 9.8 m/s²,
• $t$ is the time we want to find.

Substituting the known values into the equation, we have:

$0=20+189t-\frac{1}{2}(9.8)t^2$

This is a quadratic equation in $t$, so we can solve it using the quadratic formula:

t=−b±b2−4ac2at = frac{ -b pm sqrt{b^2 - 4ac}}{2a}t=<span class="mspace" style="margin-right