To successfully catch the cheerleader, the upward force exerted by the people catching her must be sufficient to counteract both her weight and any additional forces due to her motion (like momentum) when she is caught.
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Weight of the Cheerleader: The weight (W) of the cheerleader can be calculated using the formula: \[ W = mg \] where \( m = 45 , \text{kg} \) is her mass, and \( g \approx 9.81 , \text{m/s}^2 \) (acceleration due to gravity).
Thus,
\[ W = 45 , \text{kg} \times 9.81 , \text{m/s}^2 = 441.45 , \text{N} \] -
Exerting Force to Catch: The cheerleader exerts a downward force of 950 N. For her to be caught safely, the catchers need to exert an upward force that at least balances this downward force.
Taking this into account:
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Option A: "The people catching the cheerleader should exert an upward force of 950 N on her" – This is correct. They need to match the cheerleader's force.
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Option B: "The people catching the cheerleader should exert an upward force equal to her weight" – This is not correct because her weight alone (441 N) is not enough to counter the 950 N she exerts downwards.
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Option C: "The people catching the cheerleader should exert an upward force of about 441 N on her" – This is too low to catch her effectively, as it does not match the force she exerts.
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Option D: "The people catching the cheerleader should not exert a force on her but just stop her motion" – This doesn't make sense as stopping her motion requires an exerted force to be applied.
Conclusion: The best choice is A: "The people catching the cheerleader should exert an upward force of 950 N on her." This ensures that they match the force exerted by the cheerleader, allowing her to be successfully caught.