math geniuses?

Question

i do not get how to do this math problem at all (trig)
From a point 1.5 mi from a launch pad at cape canaveral, an observer sights a space shuttle at an angel of 10 degrees moments after its launched. After 10s the angel of elevation is 50 degrees.
a) How far does the space shuttle travel vertically during the 10s interval?
b) What is the average speed of the space shuttle during that time interval?
thank you so much

Answer 1

Imagine a right triangle with a base of 1.5 miles. The shuttle is launched straight up (forming the height of the triangle) and the observer is at the vertex of the base and hypotenuse.

When the observer first looks, the shuttle's height is unknown, but the angle is 10°. The hypotenuse is useless in this problem, and the trig ratio using the opposite side (height = h) and the adjacent side (base = 1.5) is the tangent.

tan(10°) = h / 1.5, or
h = 1.5[tan(10°)]
h = 1.5[0.17632698]
h = 0.26449047.
The shuttle is 0.26449047 miles up.

When the observer looks the second time, the angle of elevation is 50°. Do the same math.

tan(50°) = h / 1.5, or
h = 1.5[tan(50°)]
h = 1.5[1.19175359]
h = 1.787630385.
The shuttle is 1.787630385 miles up.

Now we can answer your questions.

a) How far does the shuttle travel? Subtract.
1.787630385 - 0.26449047 = 1.523139915 miles.

b) What is the average speed? Speed = Distance / Time.
1.523139915 miles / 10 seconds = 0.1523139915 miles per second. If you need that in miles per minute, multiply by 60: 60(0.1523139915) = 9.13883949 miles per minute. Need it in mph? Multiply by 60 again. 60(9.13883949) = 548.3303694 miles per hour.

Answer 2

Hi,
The distance travelled is this:
d = Height at 50 degrees - height at 10 degrees
= 1.5 (tan 50 - tan 10)
= 1.5( 1.192 -0.176)
= 1.52 miles

b) Average speed or velocity is:
v = d/t
= 1.52/10
=.152 mi/s
OR
v = 3600*0.152
=548.33 mi/h

Definitely not a math genius.

Answer 3

I normally would help you, but since you're asking for every single answer to thirty problems, that just tells me you posted your entire homework for someone else to do for you. By the time you finished typing these up, you could've been done with it. Stop being so lazy. These problems are so basic it's not even funny. Guess that makes everyone a genius.