Answer:
a) On the distant planet, the ball will travel 395 m horizontally.
b) On the distant planet, the max-height will be 48.3 m.
Explanation:
The equation for the position of an object moving in a parabolic trajectory is the following:
r = (x0 + v0 • t • cos θ, y0 + v0 • t • sin θ + 1/2 • g • t²)
Where:
r = vector position at time t
x0 = initial horizontal position
v0 = initial velocity
t = time
θ = launching angle
y0 = initial vertical position
g = acceleration due to gravity
a) First, let´s calculate the horizontal distance traveled as if we would be on earth. For this, we have to find the magnitude of the vector "r" in the figure. Seeing the figure, we know that the y-component of the vector "r" is 0 if we place the center of the frame of reference at the launching point.
Then, using the equation for the y-component of "r":
y = y0 + v0 • t • sin θ + 1/2 • g • t² (y0 = 0)
0 m = 44.4 m/s · t · sin 26° - 1/2 · 9.8 m/s² · t²
4.9 m/s² · t² = 44.4 m/s · t · sin 26°
t = 44.4 m/s · sin 26° / 4.9 m/s²
t = 3.97 s
Now, we can calculate the x-component of the vector position at final time:
x = x0 + v0 • t • cos θ (x0 = 0)
x = 44.4 m/s · 3.97 s · cos 26° = 158 m
On the distant planet, the ball will travel 158 m · 2.50 = 395 m horizontally.
b) Since the trajectory is parabolic, the maximum height will be reached at the half of the flight. Then, the maximum height will be at t = 3.97 s/2 = 1.99 s.
The max-height on earth wuould be:
y = y0 + v0 • t • sin θ + 1/2 • g • t² (y0 = 0)
y = 44.4 m/s · 1.99 s · sin 26° - 1/2 · 9.8 m/s² · (1.99 s)²
y = 19.3 m
On the distant planet the max-height will be 19.3 m · 2.50 = 48.3 m
Recall that average velocity is equal to change in position over a given time interval,
so that the <em>x</em>-component of is
and its <em>y</em>-component is
Solve for and
, which are the <em>x</em>- and <em>y</em>-components of the copter's position vector after <em>t</em> = 1.60 s.
Note that I'm reading the given details as
so if any of these are incorrect, you should make the appropriate adjustments to the work above.
Answer:
1.01 × 10⁵ Pa
Explanation:
At the surface, atmospheric pressure is 1.013 × 10⁵ Pa.
We need to find the total pressure on the air in the lungs of a person to a depth of 1 meter.
Pressure at a depth is given by :
Where
is the density of air,
So,
Total pressure, P = Atmospheric pressure + 12 Pa
= 1.013 × 10⁵ Pa + 12 Pa
= 1.01 × 10⁵ Pa
Hence, the total pressure is 1.01 × 10⁵ Pa.