Question

Hello,

Please check my answers to the questions below are correct and please help me with the question that I could not answer on my own.

Thank you so much for your time.

1. Batman is trying out a new jet propulsion pack to help him get to Gotham City's crime scenes more quickly. He knows that the scene of the crime is 3 blocks to the east and 1 block to the north of his current position, but the jet pack wants him to input an angle to plot his course. Since Gotham's blocks are on a rectangular grid, inverse trigonometry to the rescue! Round to the nearest tenth: In degrees in standard position, Batman should input an angle of 18.4 degrees. As a true bearing angle in degrees, Batman should input an angle of degrees.

Answer 1

Solution-

(1)

According to question,

Let Gotham City's crime scene is located at A (3 blocks east and 1 block south) with respect to the position of Batman (B).

As shown in figure below-

N We BI 3 units 1 unit р q A u

Now,

(a)

Batman should input at an angle of

p =tan^-1(1/3) ≈ 18.4°

(Your answer is correct).

(b)

Since bearing is taken from North to East.

In terms of bearing the Batman should input at

q = 90° - 18.4° = 71.6° .

(3)

According to question, let the position of plane is denoted by A just 150 feet above point B which is 975 feet away from the start of runway C.

As shown in figure below-

plane 1501 B gas feet

Now,

Here, angle of elevation is p (shown in figure)

So, to have safe landing angle of elevation must be small (decrease).

Since p = tan^-1(Base/height)

So, as the distance from the start of the runway increases.So, the angle increases and have a safe landing.

Hence, For safe landing-

Decrease the elevation

Increase the distance from the start of the runway.

(Your anwer are correct).