Question

15. A toy car rolls off tables of various heights at
different speeds as shown.
3.0 m/s
3.2 m/s
4.0 m/s
to
b.
fi
c. R
es
17. The
the
rule
1.0 m
0.8 m
A 10.6 m
B
C
resu
a. Rank them for the time in the air, from
greatest to least.
b. Rank them for horizontal range, from
greatest to least.
A

Answer 1

A ball in free fall is acted only by gravity, and the time in the air can be fond from the kinematic equations

a. The ranks of the balls by time spent in the air are;

Time spent by Ball C > Time spent by Ball A > Time spent by Ball B

b. The rank of the balls by range are;

Range of Ball C > Range of Ball A > Range of Ball B

Reason:

The data in table in the question appeared to have not been entered correctly

The given data may be presented as follows, and range of each ball at each height are calculated in the conclusion;

$\begin{array}{ccc}&Speed \ (m/s)&Height \ (m)\\A&3.0&1.0\\B&3.2&0.8\\C&4.0&10.6\end{array}\right]$

The time, t, taken to fall from a given height is presented as follows;

$t = \sqrt{\dfrac{2 \cdot h}{g} }$

Where;

h = The height

g = Acceleration due to gravity ≈ 9.81 m/s²

Therefore, from a height of 1 meters, we have

$t = \sqrt{\dfrac{2 \times 1}{9.81} } \approx 0.452$

Time in the air, t ≈ 0.452 s

At a 0.8 meter height, we have;

$t = \sqrt{\dfrac{2 \times 0.8}{9.81} } \approx 0.404$

Time in the air, t ≈ 0.404 s

At a 2 meters height, we have;

$t = \sqrt{\dfrac{2 \times 10.6}{9.81} } \approx 1.47$

Time in the air, t ≈ 1.47 s

Calculations of the time and range at different heights:

Range of the balls at height, h = 1.0 meters

$\begin{array}{ccc}Speed \ (m/s)&Height \ (m)& Range \ (m)\\3.0&1.0&1.356\\3.2&1.0&1.446\\4.0&1.0&1.808\end{array}\right]$

Range of the balls at height, h = 0.8 meters

$\begin{array}{ccc}Speed \ (m/s)&Height \ (m)& Range \ (m)\\3.0&0.8&1.212\\3.2&0.8&1.293\\4.0&0.8&1.616\end{array}\right]$

Range of the balls at height, h = 10.6 meters

$\begin{array}{ccc}Speed \ (m/s)&Height \ (m)& Range \ (m)\\3.0&10.6&4.41\\3.2&10.6&4.704\\4.0&10.6&5.88\end{array}\right]$

Therefore, at each height level, the time spent in the air by each ball is the same, however, the range covered by the ball moving with a higher horizontal speed is more than that of a ball moving with lower speed

a. The rank for the time spent in the air are;

$\begin{array}{ccccc}Ball &Speed \ (m/s)&Height \ (m)&Time \ (s)& Range \ (m)\\A&3.0&1.0&0.452&1.356\\B&3.2&0.8&0.404&1.293\\C&4.0&10.6&1.47&5.88\end{array}\right]$

Time spent by Ball C > Time spent by Ball A > Time spent by Ball B

b. The rank of the balls by range are;

Range of Ball C > Range of Ball A > Range of Ball B

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