A high-jumper clears the bar and has a downward velocity of -6.00 m/s just before landing on an air mattress. The mass of the high-jumper is 50.4 kg. What is the magnitude and direction of the impulse that the air mattress exerts on her? Assume that upward is the positive direction.
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To find the magnitude and direction of the impulse that the air mattress exerts on the high-jumper, we need to use the equation for impulse:
Impulse = change in momentum
Impulse is defined as the force applied multiplied by the time interval it acts. In this case, we know the mass of the high-jumper, the initial and final velocities, and we need to find the force applied by the air mattress.
Step 1: Calculate the change in momentum.
The initial momentum is given by:
p_initial = m * v_initial
where m is the mass (50.4 kg) and v_initial is the initial velocity (0 m/s since it is just before landing).
The final momentum is given by:
p_final = m * v_final
where v_final is the final velocity (-6.00 m/s) and the negative sign indicates the downward direction.
Change in momentum = p_final - p_initial
Step 2: Calculate the force applied by the air mattress.
Remember that impulse is equal to force multiplied by time, so we can rewrite the impulse equation as:
Impulse = F * Δt
Impulse = Change in momentum
Now we can rearrange the equation to find the force applied by the air mattress:
F = Impulse / Δt
Since we don't have the time interval (Δt) provided in the question, we cannot directly calculate the force. We need more information about the time it takes for the high-jumper to land on the air mattress to determine the force applied.
Therefore, without the time interval, we cannot determine the magnitude and direction of the impulse that the air mattress exerts on the high-jumper.