Solve the Problem $\mathrm { f } ( \mathrm { t } ) = 4 + 130 \mathrm { t } - 4.9 \mathrm { t } ^ { 2 }$

question 34

Multiple Choice

Solve the problem.
-An arrow is shot straight up from level ground. The distance (in meters) of the arrow above the ground (the position function) is $\mathrm { f } ( \mathrm { t } ) = 4 + 130 \mathrm { t } - 4.9 \mathrm { t } ^ { 2 }$ at any time $\mathrm { t }$ (in sec) . Find $\mathrm { f } ^ { \prime } ( 1 )$ and the initial velocity of the arrow.

• A) \(\mathrm { f } ^ { \prime } ( 1 ) = 120.2\); initial velocity \(= 130 \mathrm {~m} / \mathrm { s }\)
• B) \(\mathrm { f } ^ { \prime } ( 1 ) = 124.2\); initial velocity \(= 130 \mathrm {~m} / \mathrm { s }\)
• C) \(f ^ { \prime } ( 1 ) = 120.2\); initial velocity \(= 4 \mathrm {~m} / \mathrm { s }\)
• D) \(f ^ { \prime } ( 1 ) = - 9.8\); initial velocity \(= 130 \mathrm {~m} / \mathrm { s }\)

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Definitions:

Social Loafing

The phenomenon whereby individuals reduce their effort when working in a group compared to when working alone, due to perceived diffusion of responsibility.

Audience Effect

The impact on an individual's performance when they are aware they are being observed by others.

Co-action Effect

A phenomenon where the presence of others engaged in the same task can improve individual performance.

Social Facilitation

The tendency for people to perform differently when in the presence of others than when alone, typically improving on well-practiced tasks.