# physics

which one is angle will give the longest range ? 30 degrees ? 45 degrees ? 60 degrees ?

1. 👍 0
2. 👎 0
3. 👁 34
1. It depends on the initial height. However, if initial height = 0, then 45 degrees will give you the longest distance.

1. 👍 0
2. 👎 0
posted by Max
2. range= VcosTheta*time
timeinair:
hf=ho+VisinTheta*t-1/2 g t^2

or 1/2 gt^2-ViSinTheta*t+(hf-ho)=0
and you solve for t. Clearly, the hf-ho term at first glance seems to matter. Lets check it.

t= (ViSinTheta+-sqrt(Vi^2Sin^2Theta-2g(hf-ho))/g

taking the + sqrt solution, put that into the horizontal equation..

range=VicosTheta(ViSinTheta/g +sqrt(Vi^2sin^2theta-2(hf-ho)/g)

now,with the assistance of calculus, maximizing range (drange/dtheta =0

0=Vi^2 [sin^2theta/g - cos^2theta/g)+1/2 1/sqrt( ) *2sinthetacostheta)

and you solve for theta

and the solution is a lot of algebra, but what I want to point out, the factor (Hf-ho) is in that squareroot function in the denominator,so as Max points out, it matters the difference in height.

1. 👍 0
2. 👎 0

## Similar Questions

1. ### Math

What's the value of the missing angle *picture of a triangle and square put together which basically makes a hexagon. angles are 90 degrees, 90 degrees, 130 degrees, 130 degrees. I have to find the last angle.* A. 50 degrees B. 60

asked by Anonymous on February 5, 2015
2. ### geometry

Prove that if angle DAC is 40 degrees and angle ACD is 35 degrees, then angle BDA is 70 degrees. Write a two column proof showing statements and reasons. My teacher said my answer was wrong because BCA cannot equal 40 degrees

asked by alexandria on April 30, 2013
3. ### Math

1. Hannah drew a pattern using only equilateral triangles. Which of the following statements about the angles is an equilateral triangle is true? A. The measurement of each angle is 60 degrees** B. The measurement of each angle is

asked by Megan on February 25, 2016
4. ### Geometry

List the sides of the triangle in order from longest to shortest. Angle D is 86 degrees Angle F is 50 degrees Angle E is 44 degrees *xy=segment* A) EF, FD, DE B) FD, DE, EF C) EF, DE, FD D) DE, FD, EF My answer: I think it would

asked by Unknown on December 7, 2016
5. ### Math

Which of the following values best approximates of the length of c in triangle ABC where c = 90(degrees), b = 12, and B = 15(degrees)? c = 3.1058 c = 12.4233 c = 44.7846 c = 46.3644 In triangle ABC, find b, to the nearest degree,

asked by Max on January 26, 2018
6. ### Math

Please don't give me links to websites. Which equation can be used to find the measure of an angle that is supplementary to angle POS? A.m angle POS + m angle POQ = 108 degrees B.m angle POS + m angle POR = 108 degrees C.m angle

7. ### maths

The four angles of a pentagon is 40 degrees ,75 degrees ,125 degrees and 135 degrees .the measure of the fifth angle is ? give the solution how its came

asked by poojitha on August 29, 2015
8. ### math

i need help on unit 1 lesson 10 Geometry unit test. Name a pair of complementary angle.

asked by helllllppppp on February 27, 2019
9. ### math

Express each of the following in terms of another angle between 0 degrees and 180 degrees a. sin 50 degrees b. sin 150 degrees c. cos 45 degrees d. cos 120 degrees please explain to me how to answer this question you don't have to

asked by becky on September 1, 2016
10. ### Math

If d represents the measure of an acute angle,write an inequality to show the range of degrees. AT first I thought it was: d is less than 90 degrees, which is less than 180 degrees, but it was obviously wrong as explained by my

asked by Hannah Moraf on May 2, 2016

More Similar Questions