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A student performs an experiment to dete...

A student performs an experiment to determine how the range of a ball depends on the velocity with which it is projected. The "range" is the distance between the points where the ball lends and from where it was projected, assuming it lands at the same height from which it was projected. It each trial, the student uses the same baseball, and launches it at the same angle. Table shows the experimental results.
`|{:("Trail","Launch speed" (m//s),"Range"(m)),(1,10,8),(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 `v_(0)` according to the following equation : `R=Cv_(0)^(n)`, where C is a constant and n is another constant.
Based on this data, the best guess for the value of n is :-

A

`1/2`

B

`1`

C

`2`

D

`3`

Text Solution

Verified by Experts

The correct Answer is:
C
`R=Cv_(0)^(n)`
Putting data from table: `8=Cxx10^(n)`
`rArr 31.8=Cxx20^(n)rArr 31.8/8=3.9 cong 4=2^(n) rArr n=2`
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A student performs an experiment to determine how the range of a ball depends on the velocity with which it is projected. The "range" is the distance between the points where the ball lends and from where it was projected, assuming it lands at the same height from which it was projected. It each trial, the student uses the same baseball, and launches it at the same angle. Table shows the experimental results. |{:("Trail","Launch speed" (m//s),"Range"(m)),(1,10,8),(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 v_(0) according to the following equation : R=Cv_(0)^(n) , where C is a constant and n is another constant. The student speculates that the constant C depends on :- (i) The angle at which the ball was launched (ii) The ball's mass (iii) The ball's diameter If we neglect air resistance, then C actually depends on :-

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