Kinematics Problems 5&6 Solutions
5) Juan drops a rock off of a cliff and watches it fall.
a) If the rock is moving at a speed of 30 m/s just before it hits the ground, what is the
rock’s average speed?
𝒎
𝒎
𝒗𝟏 + 𝒗𝟐 𝟎 𝒔 + 𝟑𝟎 𝒔
𝒎
̅=
𝒗
=
= 𝟏𝟓
𝟐
𝟐
𝒔
b) If the height of the cliff 45.9 meters, how long did it take the rock to fall?
Even though the rock is accelerating throughout its fall, we can use the average
velocity to find time of fall.
𝒙 𝟒𝟓. 𝟗 𝒎
𝒕= =
𝒎 = 𝟑. 𝟎𝟔 𝒔
𝒗
𝟏𝟓
𝒔
c) What is the rock’s acceleration throughout its fall?
𝒎
𝟑𝟎 𝒔
𝒄𝒉𝒂𝒏𝒈𝒆 𝒊𝒏 𝒗𝒆𝒍𝒐𝒄𝒊𝒕𝒚
∆𝒗
𝒎
𝒂𝒄𝒄𝒆𝒍𝒆𝒓𝒂𝒕𝒊𝒐𝒏 =
→𝒂=
=
= 𝟗. 𝟖 𝟐
𝒄𝒉𝒂𝒏𝒈𝒆 𝒊𝒏 𝒕𝒊𝒎𝒆
∆𝒕 𝟑. 𝟎𝟔 𝒔
𝒔
The acceleration is downward, toward the earth.
6) Jenna drops a bowling ball off of the Sears Tower.
a) If the bowling ball is moving at a speed of 102 m/s just before it hits the ground, what
is the bowling ball’s average speed?
𝒎
𝒎
𝒗𝟏 + 𝒗𝟐 𝟎 𝒔 + 𝟏𝟎𝟐 𝒔
𝒎
̅=
𝒗
=
= 𝟓𝟏
𝟐
𝟐
𝒔
b) If the height of the Sears Tower is 529 meters (1729’), how long did it take the
bowling ball to fall?
𝒙 𝟓𝟐𝟗 𝒎
𝒕= =
𝒎 ≈ 𝟏𝟎. 𝟒 𝒔
𝒗
𝟓𝟏 𝒔
c) What is the speed of the bowling ball at exactly half the total fall time?
𝒎
𝒎
Since the bowling ball is constantly increasing in speed from 𝟎 to 𝟏𝟎𝟐 , we
𝒔
𝒔
can assume that at half the fall time (5.2 s) , it has half its total speed. This is just
the average speed!
𝒎
So the answer is just 𝟓𝟏 𝒔
d) At the time in (c), has the ball fallen exactly halfway down the building? Explain
your answer. As an extra challenge, can you calculate exactly where the ball would
be at half the fall time?
No! The ball has fallen less than halfway down the building. Since the speed is increasing,
in the second half of the total time, the ball must cover more distance.
To figure out where the ball is at 𝒕 = 𝟓. 𝟐𝟓 𝒔, one must figure out the average speed for the
first half of the fall. But this is just half the average for the entire fall!
𝒎
𝒎
𝒗𝟏 + 𝒗𝟐 𝟎 𝒔 + 𝟓𝟏 𝒔
𝒎
̅=
𝒗
=
= 𝟐𝟓. 𝟓
𝟐
𝟐
𝒔
So, the ball must be at:
𝒎
̅ ∗ 𝒕 = 𝟐𝟓. 𝟓 ∗ 𝟓. 𝟐 𝒔 = 𝟏𝟑𝟐. 𝟔 𝒎
𝒙=𝒗
𝒔
which is nowhere near halfway! (Halfway would be 264.5 m)