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IRISSAK [1]
2 years ago
14

If the range of a projectile's trajectory is six times larger than the height of the trajectory, then what was the angle of laun

ch with respect to the horizontal? (Assume a flat and horizontal landscape.)
Physics
1 answer:
zvonat [6]2 years ago
3 0

Answer:

H = 1/2 g t^2    where t is time to fall a height H

H = 1/8 g T^2   where T is total time in air  (2 t  = T)

R = V T cos θ       horizontal range

3/4 g T^2 = V T cos θ       6 H = R    given in problem

cos θ = 3 g T / (4 V)           (I)

Now t = V sin θ / g     time for projectile to fall from max height

T = 2 V sin θ / g

T / V = 2 sin θ / g

cos θ = 3 g / 4 (T / V)     from (I)

cos θ = 3 g / 4 * 2 sin V / g = 6 / 4 sin θ

tan θ = 2/3      

θ = 33.7 deg

As a check- let V = 100 m/s

Vx = 100 cos 33.7 = 83,2

Vy = 100 sin 33,7 = 55.5

T = 2 * 55.5 / 9.8 = 11.3 sec

H = 1/2 * 9.8 * (11.3 / 2)^2 = 156

R = 83.2 * 11.3 = 932

R / H = 932 / 156 = 5.97        6 within rounding

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Norma-Jean [14]

The actual distance of Regulus from Earth is 23.81 parsecs.

Given:

Parallax of Regulus, p = 0.042 arc seconds

Calculation:

When an observer changes their position, an apparent change in the object's position takes place. This change can be calculated using the angle ( or semi-angle) made by the observer and object i.e. the angle made between the two lines of observation from the object to the observer.

Thus from the relation of parallax of a celestial body we get:

S = 1/ tan p ≈ 1 / p

where S is the actual distance between the object and the observer

            p is the parallax angle observed

Here for Regulus, we get:

S = 1 / p

  = 1 / (0.042)                                     [ 1 parsecs = 1 arcseconds ]

  = 23.81 parsecs

We know that,

1 parsecs = 3.26 light-years = 206,000 AU

Converting the actual distance into light years we get:

23.81 parsecs = 23.81 × (3.26 light yrs) = 77.658 light-years

Therefore, the actual distance of Regulus from Earth is 23.81 parsecs which is 77.658 in light years.

Learn more about astronomical units here:

<u>brainly.com/question/16471213</u>

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6 0
1 year ago
50g of ice at 0°C is mixed with 50g of water at 80°C, what will be the final temperature of a mixture in
xxTIMURxx [149]

Answer:

0° C

Explanation:

Given that

Mass of ice, m = 50g

Mass of water, m(w) = 50g

Temperature of ice, T(i) = 0° C

Temperature of water, T(w) = 80° C

Also, it is known that

Specific heat of water, c = 1 cal/g/°C

Latent heat of ice, L(w) = 89 cal/g

Let us assume T to be the final temperature of mixture.

This makes the energy balance equation:

Heat gained by ice to change itself into water + heat gained by melted ice(water) to raise its temperature at T° C = heat lost by water to reach at T° C

m(i).L(i) + m(i).c(w)[T - 0] = m(w).c(w)[80 - T], on substituting, we have

50 * 80 + 50 * 1(T - 0) = 50 * 1(80 - T)

4000 + 50T = 4000 - 50T

0 = 100 T

T = 0° C

Thus, the final temperature is 0° C

3 0
2 years ago
Why might a balloon, that is inflated almost to its capacity, pop or explode on an extremely warm day?
REY [17]
On an extremely warm day, the balloon might pop because gases expand the hotter they get, and due to its temperature it is likely to pop if it is, indeed, nearly, if not completely, filled to its capacity.  I hope this helps, have a nice day!
7 0
3 years ago
Read 2 more answers
Estimate the radiation pressure due to a bulb that emits 25 W of EM radiation at a distance of 6.5 cm from the center of the bul
Deffense [45]

..........................................................

8 0
2 years ago
Compute the power output (watts) during one minute of treadmill exercise, given the following: Treadmill grade-10% Horizontal sp
erma4kov [3.2K]

Answer:

c. 981 watts

P=981\ W

Explanation:

Given:

  • horizontal speed of treadmill, v=100\ m.min^{-1}=\frac{5}{3} \ m.s^{-1}
  • weight carried, w=588.6\ N
  • grade of the treadmill, G\%=10\%

<u>Now the power can be given by:</u>

P=v.w

P=588.6\times\frac{5}{3} (where grade is the rise of the front edge per 100 m of the horizontal length)

P=981\ W

6 0
3 years ago
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