Angle of a projectile
Favorites|Homepage
Subscriptions | sitemap
HOME > Physics > Angle of a projectile

Angle of a projectile

[From: ] [author: ] [Date: 11-09-24] [Hit: ]
Take upwards as positive, Vi is initial velocity, xi and yi will be the initial position of the projectile, A will be the angle of the projectile with horizontal.When the projectile is at its max. height,......
Find the angle of projection at which the horizontal range and the maximum height of a projectile are equal.

So, this is my work, but I got the answer wrong, and I don't know what I did wrong. Can you please point out for me ?

Take upwards as positive, Vi is initial velocity, xi and yi will be the initial position of the projectile, A will be the angle of the projectile with horizontal.
When the projectile is at its max. height, its Vy = 0, so we have
(Vi sinA) - gt = 0 ---------> (Vi sinA) = gt (1)

Horizontal range of the projectile is
x = xi + (Vi cosA)t
x = (Vi cosA)t

Max. height is
y max = yi + (Vi sinA)t - (1/2) gt^2
y max = (Vi sinA)t - (1/2) gt^2
Also, we are given that x = y max. so
(Vi cosA)t = (Vi sinA)t - (1/2) gt^2

since t will be not equal to 0, we can divide t
(Vi cosA) = (Vi sinA) -(1/2) gt (2)

From (1), we can replace (Vi sinA) = gt, so (2) will become
(Vi cosA) = (Vi sinA) - (1/2)(Vi sinA)

(Vi cosA) = (1/2)(Vi sinA)

sinA / cosA = 2

tan A = 2

A = 63.4 degrees

However, the answer is tan A = 4, and A = 76 degrees.....

-
The time you use for y max is the half the time for the range.
Horizontal range of the projectile is
x = (Vi cosA) (2t) Note the number 2 in this equation.

Now proceed and get the correct value.
================================

The formula for range R = u^2 sin 2θ /g and
The formula for height is H = u^2 (sinθ)^2 /2g
If R = H

u^2 sin 2θ /g = u^2 (sinθ)^2/ 2g

Canceling u^2/ g on both sides
2 sin θ* cos θ = (sinθ) ^2 /2
tan θ = 4
=========================
1
keywords: Angle,projectile,of,Angle of a projectile
New
Hot
© 2008-2010 http://www.science-mathematics.com . Program by zplan cms. Theme by wukong .