Disregarding air drag, how fast must you toss a ball straight up in order for it to take 2 seconds to return to the level from which you tossed it?
A) 10 m/s
B) 20 m/s
C) 15 m/s
D) 5 m/s
E) 7.5 m/s

Question

Quizplus · Accepted Answer

The ball takes 1 second to reach the peak of its trajectory, where its velocity is 0 m/s. Using the formula $v = u + at$, where $v$ is the final velocity (0 m/s at the peak), $u$ is the initial velocity, $a$ is the acceleration due to gravity (-9.8 m/s$^2$, negative because it's acting in the opposite direction of the toss), and $t$ is the time (1 second to reach the peak), we can solve for $u$: $0 = u - 9.8 \times 1$, giving $u = 9.8 m/s$. However, since the question asks for the speed to return to the level from which it was tossed, we consider the speed at the moment of the toss, which needs to be enough to reach the peak and return, effectively doubling the time in the air to 2 seconds. The correct calculation should directly use the total time of 2 seconds, where the speed needed is $9.8 m/s^2 \times 1 s = 9.8 m/s$, but since we're looking for an answer in the options provided, 10 m/s is the closest correct answer, allowing for the ball to reach the peak and return in 2 seconds.

Disregarding Air Drag, How Fast Must You Toss a Ball