Answer:
(a) 62.5 m
(b) 7.14 s
Explanation:
initial speed, u = 35 m/s
g = 9.8 m/s^2
(a) Let the rocket raises upto height h and at maximum height the speed is zero.
Use third equation of motion
h = 62.5 m
Thus, the rocket goes upto a height of 62.5 m.
(b) Let the rocket takes time t to reach to maximum height.
By use of first equation of motion
v = u + at
0 = 35 - 9.8 t
t = 3.57 s
The total time spent by the rocket in air = 2 t = 2 x 3.57 = 7.14 second.
Answer:
x = 0.0734 m = 7.34 cm
Explanation:
First we shall calculate the area of the piston:
Now, we will calculate the force on the piston due to atmospheric pressure:
Now, for the compression of the spring we will use Hooke's Law as follows:
where,
k = spring constant = 3400 N/m
x = compression = ?
Therefore,
<u>x = 0.0734 m = 7.34 cm</u>
Answer:
θ = 19.66°
Explanation:
To determine the angle that the rope makes with the vertical for the two people, you first take into account the potential energy of the first person before he swings on the rope:
h: distance to the ground
g: gravitational acceleration = 9.8m/s^2
m: mass of the first person = 55 kg
In the image attache below you can notice that the height h is:
Then, the potential energy is:
When the first person picks up the second person (when the rope is exactly vertical), all the potential energy becomes kinetic energy. Next, when both people reaches the maximum height h' the energy must be equal to the initial potential energy of the first person:
From the previous equation you can get h':
Finally, you obtain the angle between the rope at the height h,' and the vertical, by calculating the following:
hence, the angle between the rope and the vertical, when the two people are in the rope is 19.66°
