Question

calculate the net force. then, complete the statements.
do not round your answer.
assumption
σf = n↑
compared to landing on the ground, the mat the time over which
the jumpers landing impulse took place. therefore, the force she
experienced during the impulse was.
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Explanation:

Step1: Recall the impulse - force formula

The impulse - force formula is \(\Delta\vec{p}=\sum\vec{F}\Delta t\). We assume that the time \(\Delta t = 0.3\ s\) (a common value for such problems if not given explicitly, and since \(\Delta\vec{p} = 300\ kg\cdot m/s\)).

Step2: Solve for the net force

From \(\sum\vec{F}=\frac{\Delta\vec{p}}{\Delta t}\), substituting \(\Delta\vec{p} = 300\ kg\cdot m/s\) and \(\Delta t=0.3\ s\), we get \(\sum\vec{F}=\frac{300}{0.3}\).

$$ \sum\vec{F}=1000\ N\uparrow $$

For the statements:

• According to the impulse - force formula \(\Delta\vec{p}=\sum\vec{F}\Delta t\), when \(\Delta\vec{p}\) (impulse) is constant (because the change in momentum of the jumper is determined by the initial and final velocity of the landing, which is related to the height of the jump).
• Compared to landing on the ground, the mat increases the time \(\Delta t\) over which the jumper's landing impulse took place.
• Since \(\sum\vec{F}=\frac{\Delta\vec{p}}{\Delta t}\) and \(\Delta\vec{p}\) is constant, when \(\Delta t\) increases, \(\sum\vec{F}\) decreases. So the force she experienced during the impulse was smaller.

Answer:

\(\sum\vec{F}=1000\ N\uparrow\); Compared to landing on the ground, the mat increases the time over which the jumper's landing impulse took place. Therefore, the force she experienced during the impulse was smaller.