Physics prob... need some help

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caveman721

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Can anyone help me with this physics prob, can you show me the explation as well as the math steps to solve this one.

Thank you

A student performs an experiment to determine how the range of a ball depends on the velocity with which it is released. The “range” is the distance between where the ball lands and where it was released, assuming it lands at the same height from which it was released.

In each trial, the student uses the same baseball, and launches it at the same angle. Table 1 shows the experimental results.

TABLE 1
Trial launch speed (m/s) range (m)
1 10 8.0
2 20 31.8
3 30 70.7
4 40 122.5

Based on this data, the student then hypothesizes that the range, R, depends on the initial speed, v0, according to the following equation:
R = C
9f3c0001.jpg
,

where C is a constant, and n is another constant.





1.Based on this data, the best guess for the value of n is
A.1/2
B.1
C.2
D.3
it says the answer is "C" but why and how.

Thanks again

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If i understand the question correctly then the answer is simple. They've given an equation w/ two constants (C, n), and asked to solve for one constant by providing more than 1 values of the remainder 2 variables (R, vo) in the equation.

So, plugging in first inputs from table gives us
eq#1: 8 = C(10)^n

Taking second input from the table gives us
eq#2: 31.8 = C(20)^n

dividing #1 by #2 gives us

31.8/8 = 2^n
~32/8 = 2^n
4 = 2^n
therefore, n = 2
 
no way hahaha i thought the way it looked like in the equation i thought Vo was an power to C, not its own variable. wow thanks
 
i thought the way it looked like in the equation i thought Vo was an power to C, not its own variable.

it very well may be... but won't know w/o actually seeing it... if you are using a practice book, perhaps an explanation may have been provided ;)
 
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