Help for “Freefall #2”:

An empty can of paint falls from the top of a 6-foot (1.8-meter) tall ladder.

givens: v_i=0, a = –9.8 m/s², Dx=–1.8 m

how fast? v_f = ? m/s

v_f² = v_i² +2a Dx

how much time? t=?s

Dx= v_it + ½at² or Dx= ½at² ( since v_i=0)

t²=2Dx/a

A stone is dropped from the top of an overhang into the river below

givens: v_i=0, a = –9.8 m/s², t=4 s

from what height? Dx = ? m

Dx= ½at² ( since v_i=0)

how fast? v_f = ? m/s

v_f = v_i +at

A bouncing superball rises to a height of 1.2 meters before returning to the ground.

givens: on the way up, Dx=1.2 m, a = –9.8 m/s², at the top v_f = 0

how fast? v_i =? m/s

v_f² = v_i² +2a Dx

v_i² = –2a Dx

total time? t=? s, if you find the time up, double it to get the whole time (t_up=t_down if Dx=0), use the same givens as above plus your answer for v_i

a = (v_f – v_i)/t

t = (v_f – v_i)/a (double this time to get whole time)

A juggler tosses a ball upwards at 6 m/sec while sitting atop a 3.5-meter tall unicycle.

givens: v_i=6 m/s, a = –9.8 m/s², at the top v_f=0

how high? Dx = ? m

v_f² = v_i² +2a Dx

Dx= –v_i²/2a

total time to hit floor, t_total=?s

now the givens are v_i=6 m/s, a = –9.8 m/s², Dx=–3.5 m (starts from top of unicycle and ends on floor)

Dx= v_it + ½at²

YIKES! you’d have to use the quadratic equation to find “t” so let’s find v_f first.

how fast when it strikes floor? v_f = ?

v_f² = v_i² +2a Dx

now that we have v_f , find time using

a = (v_f – v_i)/t

t = (v_f – v_i)/a

A 2-meter tall basketball player trapped almost under the net tosses the ball in a last second attempt to make a goal. How fast was the ball thrown if it just slides into the 3-meter basket as it reaches the apex of its trajectory?

givens: a = –9.8 m/s², at the apex (top) v_f=0, Dx = 3m–2m=1m

how fast? v_i=? m/s

v_f² = v_i² +2a Dx

v_i² = –2a Dx