Answer:
The effective spring constant of the firing mechanism is 1808N/m.
Explanation:
First, we can use kinematics to obtain the initial velocity of the performer. Since we know the angle at which he was launched, the horizontal distance and the time in which it's traveled, we can calculate the speed by:
(This is correct because the horizontal motion has acceleration zero). Then:
Now, we can use energy to obtain the spring constant of the firing mechanism. By the conservation of mechanical energy, considering the instant in which the elastic band is at its maximum stretch as t=0, and the instant in which the performer flies free of the bands as final time, we have:
Then, plugging in the given values, we obtain:
Finally, the effective spring constant of the firing mechanism is 1808N/m.
Answer:
<em>The magnitude of vector d is 16 and the angle with the x-axis is 270°</em>
Explanation:
<u>Operations With Vectors</u>
Given two vectors in rectangular components:
The sum of the vectors is:
The difference between the vectors is:
The magnitude of 
is:
The angle makes with the horizontal positive direction is:
The question provides the vectors:
Calculate:
The magnitude of 
is:
The angle is calculated by:
The division cannot be calculated because the denominator is zero. We need to estimate the correct angle by looking at the components of the vector. Since the x-coordinate is zero and the y-coordinate is negative, the vector points downwards (south), thus the angle must be -90° or 270° if the range goes from 0° to 360°.
The magnitude of vector d is 16 and the angle with the x-axis is 270°
-- pick a planet from the table
-- take it's mass and radius from the table, and plug them into the big ugly formula above the table
-- do the arithmetic with your pencil or your calculator. The answer is the acceleration of gravity on the planet you picked. Write it down so you don't lose it.
-- do the same for the other 3 planets in the table
