A ball is thrown upward. Neglecting air resistance, what initial upward speed does the ball need to remain in the air for a total time of 10 s?

Question

Quizplus · Accepted Answer

The total time the ball spends in the air is twice the time it takes to reach its peak height, as the ascent and descent times are equal. Using the formula $t = \frac{v}{g}$ for the ascent, where $v$ is the initial velocity and $g$ is the acceleration due to gravity (approximately $9.8 \, \text{m/s}^2$), we find the time to reach the peak is $5 \, \text{s}$ (half of $10 \, \text{s}$). Therefore, the initial speed needed is $v = g \times t = 9.8 \, \text{m/s}^2 \times 5 \, \text{s} = 49 \, \text{m/s}$, which is closest to $50 \, \text{m/s}$.

A Ball Is Thrown Upward