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 53.7 kg. What is the magnitude and direction of the impulse that the air mattress exerts on her? Assume that upward is the positive direction.
impulse=change of momentum
impulse=mass(final velocity-intial velocity)
= 53.7(6) kg m/s
Well, it seems like the high-jumper is experiencing a real "downfall" here! Let's calculate the magnitude and direction of the impulse.
To calculate the impulse, we need to use the equation:
Impulse = Change in momentum
Since momentum is given by:
Momentum = mass × velocity
The initial momentum of the high-jumper just before landing can be calculated as:
Initial momentum = mass × initial velocity
Since the high-jumper's initial velocity is the downward velocity of -6.00 m/s, the initial momentum would be:
Initial momentum = 53.7 kg × (-6.00 m/s)
Now, to find the final momentum, we need to consider that the direction changes to upward after landing on the air mattress.
Final momentum = mass × final velocity
Since the final velocity is upward, it can be considered positive. Therefore, the final momentum would be:
Final momentum = 53.7 kg × (positive final velocity)
Now, since the impulse is the change in momentum, we can calculate it as:
Impulse = Final momentum - Initial momentum
The magnitude of the impulse will be the absolute value of the calculated impulse. The direction of the impulse will depend on whether the impulse is positive or negative.
So, as a humorous twist, imagine the impulse shouting "Hey high-jumper, I'm changing your direction!" with a positive magnitude if it's positive and a negative magnitude if it's negative.
But let's put humor aside for a moment and calculate the impulse:
Impulse = Final momentum - Initial momentum
Now, I can't calculate the exact impulse without knowing the final velocity. So, if you let me know the final velocity, I'll be happy to give you a more precise answer!
To find the impulse exerted by the air mattress on the high-jumper, we can use the impulse-momentum principle.
The impulse is defined as the change in momentum, which can be calculated using the equation:
Impulse = (Final momentum) - (Initial momentum)
We can calculate the initial momentum of the high-jumper using the formula:
Initial momentum = mass × initial velocity
Given:
Mass of the high-jumper (m) = 53.7 kg
Initial velocity (u) = -6.00 m/s (downward, so negative)
Therefore, the initial momentum of the high-jumper is:
Initial momentum = mass × initial velocity
= 53.7 kg × (-6.00 m/s)
= -322.2 kg·m/s
Next, we need to calculate the final momentum of the high-jumper, which is when she lands on the air mattress. The final velocity is not provided, so we will assume it to be zero as the high-jumper comes to rest.
Final momentum = mass × final velocity
= 53.7 kg × 0 m/s
= 0 kg·m/s
Now, we can calculate the impulse:
Impulse = (Final momentum) - (Initial momentum)
= 0 kg·m/s - (-322.2 kg·m/s)
= 322.2 kg·m/s
The magnitude of the impulse is 322.2 kg·m/s.
Since the air mattress exerts an impulse in the opposite direction of the initial momentum, the direction of the impulse is upward.
Therefore, the magnitude of the impulse exerted by the air mattress on the high-jumper is 322.2 kg·m/s, and its direction is upward.
To find the magnitude and direction of the impulse that the air mattress exerts on the high-jumper, we need to apply the impulse-momentum principle. The impulse experienced by an object is equal to the change in momentum it undergoes.
1. First, let's find the initial momentum of the high-jumper. The momentum (p) of an object is given by the product of its mass (m) and its velocity (v).
Initial momentum, p₁ = m₁ * v₁
Since the high-jumper is moving downwards with a velocity of -6.00 m/s, the initial momentum can be calculated as:
p₁ = 53.7 kg * (-6.00 m/s) = -322.2 kg·m/s (negative because it's moving downwards)
2. Next, we need to find the final momentum of the high-jumper just before landing on the air mattress. Since the high-jumper comes to rest on the mattress, its final velocity is 0 m/s.
Final momentum, p₂ = m₂ * v₂
As the final velocity is 0 m/s, the final momentum can be calculated as:
p₂ = 53.7 kg * 0 m/s = 0 kg·m/s
3. The change in momentum (∆p) is the difference between the final and initial momentum.
∆p = p₂ - p₁
∆p = 0 kg·m/s - (-322.2 kg·m/s) = 322.2 kg·m/s (positive because the direction changes from downward to upward)
4. According to the impulse-momentum principle, the impulse experienced by an object is equal to the change in momentum it undergoes.
Impulse = ∆p = 322.2 kg·m/s
So, the magnitude of the impulse that the air mattress exerts on the high-jumper is 322.2 kg·m/s. To determine the direction, we can use the sign of the impulse. Since the impulse is positive, it means the air mattress exerts an upward impulse on the high-jumper. Thus, the direction of the impulse is upward.