projectile (2 Viewers)

[shuning]

A particle P, is projected from a point, O on level griund at an angle 60 deg, to the horizontal with initial velocity V per second
After 7 seconds the projectile's velocity is 3/4 V. ignoring air resistance and assuming acceleration due to gravity is -10

i) show that V =

 

[lolokay]

well we have our equations, velocity v at 7 seconds:
vcos@ = Vcos@ = V/2
vsin@ = Vsin@ + gt
= rt3 V/2 - 70

v² = vcos²@ + vsin²@
= V² + 70² -70 rt3 V
= (3/4 V)²
= 9/16 V²

so 7/16 V² - 70 rt3 V + 70² = 0
V² - 160rt3 V + 70*160 = 0
solve as a quadratic
V = 160rt3 /2 +- rt(160²*3 - 4*70*160)/2
= 80rt3 +- 80rt(12 - 7) /2
= 80rt2 +- 40rt5
= 40(2rt3 +- rt5)

 

[shuning]

回复: Re: projectile

well we have our equations, velocity v at 7 seconds:
vcos@ = Vcos@ = V/2
vsin@ = Vsin@ + gt
= rt3 V/2 - 70

v² = vcos²@ + vsin²@
= V² + 70² -70 rt3 V
= (3/4 V)²
= 9/16 V²

so 7/16 V² - 70 rt3 V + 70² = 0
V² - 160rt3 V + 70*160 = 0
solve as a quadratic
V = 160rt3 /2 +- rt(160²*3 - 4*70*160)/2
= 80rt3 +- 80rt(12 - 7) /2
= 80rt2 +- 40rt5
= 40(2rt3 +- rt5)

oh shit i got all the way there and then.... wrong calaulation T.T
thx very much man. u deserve a rep. since no1 those days bother to try projectile questions ( too lazy to derive all the equations? xD )