Since the rocket’s acceleration is 3.00 m/s^3 * t, its acceleration is increasing at the rate of 3 m/s^3 each second. The equation for its velocity at a specific time is the integral of the acceleration equation.
<span>vf = vi + 1.5 * t^2, vi = 0 </span>
<span>vf = 1.5 * 10^2 = 150 m/s </span>
This is the rocket’s velocity at 10 seconds. The equation for its height at specific time is the integral velocity equation
<span>yf = yi + 0.5 * t^3, yi = 0 </span>
<span>yf = 0.5 * 10^3 = 500 meters </span>
<span>This is the rocket’s height at 10 seconds. </span>
<span>Part B </span>
<span>What is the speed of the rocket when it is 345 m above the surface of the earth? </span>
<span>Express your answer with the appropriate units. </span>
<span>Use the equation above to determine the time. </span>
<span>345 = 0.5 * t^3 </span>
<span>t^3 = 690 </span>
<span>t = 690^⅓ </span>
<span>This is approximately 8.837 seconds. Use the following equation to determine the velocity at this time. </span>
<span>v = 1.5 * t^2 = 1.5 * (690^⅓)^2 </span>
<span>This is approximately 117 m/s. </span>
<span>The graph of height versus time is the graph of a cubic function. The graph of velocity is a parabola. The graph of acceleration versus time is line. The slope of the line is the coefficient of t. This is a very different type of problem. For the acceleration to increase, the force must be increasing. To see what this feels like slowly push the accelerator pedal of a car to the floor. Just don’t do this so long that your car is speeding!!</span>
Answer:
No
Explanation:
The vertical component of Jack's initial velocity is:
5.0
⋅
sin
30
∘
=
5.0
⋅
1
2
=
2.5
m/s
With gravitational acceleration
9.8
m/s
2
, he will reach the highest point of his trajectory after:
2.5
9.8
≈
0.255
s
The average vertical component of his velocity in that
0.255
s
will be:
1
2
⋅
2.5
=
1.25
m/s
So the highest point of his trajectory will be:
0.255
⋅
1.25
≈
0.32
m
So he will pass approximately
7
cm
above the top of the candle.
The horizontal component of his velocity will be a constant:
5.0
⋅
cos
30
∘
=
5.0
⋅
√
3
2
≈
4.33
m/s
So Jack's trajectory will be substantially longer than it is high and he will spend little time anywhere near above the candle.
Answer:
The pectoralis major, latissimus dorsi, deltoid, and rotator cuff muscles connect to the humerus and move the arm. The muscles that move the forearm are located along the humerus, which include the triceps brachii, biceps brachii, brachialis, and brachioradialis.
