Projectiles (1 Viewer)

[Jago]

A golf ball is hit towards a tree 60m away and standing in the same horizontal plane as the ball. The tree is 20m high. The initial V of the ball is 30 m/s

Find the range of angles, in which the ball must be hit to clear the tree. g = -10

 

[Jago]

i got up to:

-20/Cos²x + 60Sinx/cosx > 20

*shrugs*

 

[rama_v]

i got up to:

-20/Cos²x + 60Sinx/cosx > 20

*shrugs*

Presuming this is right:

-20(1+tan²x) + 60tanx - 20 = 0
-20 - 20tan²x + 60tanx - 20 = 0
20tan²x - 60tanx + 40 = 0
tan²x - 3tanx + 2 = 0
let u = tan x
u² - 3u + 2 = 0
(u-2)(u-1)=0
.: tan x = 2 or tan x = 1
45 ^o < x < tan^-1 2

 

[Jago]

fuuuucccckkkk i really should remember the trig identities

Edit: thanks buddy

 

[justchillin]

The identity: tan^2x+1=sec^2x is vital for projectile questions...
Id know them very well for the exam...

 

[StGeorgeDragons]

how do u get


-20/Cos²x + 60Sinx/cosx > 20

 

[word.]

how do u get


-20/Cos²x + 60Sinx/cosx > 20

consider vertical motion of projectile:
a = -10
v = -10t + 30sinθ
y = -5t² + 30t*sinθ --[1]

horizontal:
a = 0
v = 30cosθ
x = 30t*cosθ
so t = x/(30cosθ) --[2]

sub [1] --> [2]
y = -x²sec²θ/180 + xtanθ

at x = 60 you want y > 20
so -20sec²θ + 60tanθ > 20

 

[StGeorgeDragons]

Presuming this is right:

-20(1+tan²x) + 60tanx - 20 = 0
-20 - 20tan²x + 60tanx - 20 = 0
20tan²x - 60tanx + 40 = 0
tan²x - 3tanx + 2 = 0
let u = tan x
u² - 3u + 2 = 0
(u-2)(u-1)=0
.: tan x = 2 or tan x = 1
45 ^o < x < tan^-1 2

when i solve the inequality u² - 3u + 2 = 0 i get u less than 1 and u greater than 2. and then tanx less than 1 and tan x greater than 2. how do u get 45 ^o < x < tan^-1 2?

 

[word.]

when i solve the inequality u² - 3u + 2 = 0 i get u less than 1 and u greater than 2. and then tanx less than 1 and tan x greater than 2. how do u get 45 ^o < x < tan^-1 2?

u² - 3u + 2 = 0 isn't an inequality but anyway:

From rama's 2 lines:

-20 - 20tan2x + 60tanx - 20 = 0
20tan2x - 60tanx + 40 = 0

He multiplied by -1 here so he knows he should reverse the inequality later on...
... but there should have been inequality signs here essentially:

-20 - 20tan²x + 60tanx - 20 > 0

20tan²x - 60tanx + 40 < 0 (multiplying by negative number reverses inequality sign)

u² - 3u + 2 < 0

(u - 2)(u - 1) < 0

45° < x < tan^-12