# Question aaac7

Jul 21, 2015

Velocity: -4.0 m/s

#### Explanation:

The first thing you need to do to solve this problem is figure out whether or not the stone will be moving upwards or downwards after 0.97 seconds.

Since upward is set as positive and downward as negative, the sign of the gravitational acceleration, $g$, will have to match this convention as well.

At the top of its motion, i.e. at maximum height, the velocity of the stone will be zero. This means that you can determine the time it takes the stone to reach that height by

underbrace(v_"top")_(color(blue)("=0")) = v_i - g * t

t = v_i/g = (5.5cancel("m")/cancel("s"))/(9.8cancel("m")/"s"^cancel(2)) = "0.561 s"

After 0.561 s the stone begins to fall towards the ground. This means that the sign of the velocity after 0.97 s will be negative.

To determine its velocity, calculate the time it spends in free fall

${t}_{\text{fall" = 0.97 - 0.561 = "0.409 s}}$

The stone is in free fall for 0.409 seconds, which means that its velocity at that point in time will be

v = underbrace(v_"top")_(color(blue)("=0")) - g * t_"fall"

v = -9.8"m"/"s"^cancel(2) * 0.409cancel("s") = color(green)(-"4.0 m/s")#