Answer to Question #166610 in Mechanics | Relativity for hedaia

Question

Gerri leaves the long jump takeoff board with a vertical velocity of 2.8 m⋅s^-1 and a horizontal  velocity of 7.7 m⋅s^-1

 

a) What is Gerri’s resultant velocity at takeoff? 

b) What is Gerri’s takeoff angle - the angle of her resultant takeoff velocity with horizontal? c) What is Gerri’s horizontal velocity just before she lands? 

d) How long Gerri stayed in the air? 

e) What was her jump length? if she landed perfectly 

f) What is Gerri’s vertical velocity at the end of her flight? 

g) If Gerri’s center of gravity was 1.0 m high at the instant of takeoff, how high will it be at the  peak of her flight? 

Answer 1

$v_y=2.8~\frac ms,~v_x=7.7 ~\frac ms,$

a)

$v=\sqrt{v_x^2+v_y^2}=\sqrt{2.8^2+7.7^2}=8.19~\frac ms,$

b)

$\alpha=atan \frac{v_y}{v_x}=atan\frac{2.8}{7.7}=20°,$

c)

$v_x'=v_x=7.7 ~\frac ms,$

d)

$t=2t_0=\frac{2v_y}{g}=\frac{2\cdot 2.8}{9.8}=0.57 ~s,$

e)$s=v_x t=\frac{2v_xv_y}{g}=\frac{2\cdot 7.7\cdot 2.8}{9.8}=4.4~m,$

f)

$v_y'=v_y=2.8~ \frac ms,$

g)$h=1+(v_yt_0-\frac{gt_0^2}{2})=1+\frac{v_y^2}{2g}=1+\frac{2.8^2}{2\cdot 9.8}=1.4~m.$