## anonymous one year ago An athlete performing a long jump leaves the ground at a 33.4∘ angle and lands 7.68m away.

1. anonymous

What do you want to ask? you have provided the data.

2. anonymous

takeoff speed of the athlete

3. anonymous

|dw:1433534380042:dw| do you recall the equations for x(t) and y(t) ??

4. anonymous

i am not sure of which equations to use

5. anonymous

is it x= x= x0+Vx0t-1/2gt^2?

6. anonymous

here they are: $x(t)=x_0 + v_{0x}t$ $y(t)=y_0 + v_{0y}t - \frac{1}{2}gt^2$ the conditions are in the picture i made... try to put all that togheter...

7. anonymous

yes that was for y not x

8. anonymous

is x0 the 7.68?

9. anonymous

i am confused about which numbers are what variables

10. anonymous

x0 and y0 are the coordinates of the starting point, in this problem we can set both of them to 0. |dw:1433535031686:dw|

11. anonymous

and xt?

12. anonymous

x(t) is the value x takes at time t. we know that for some value of time x(t)=7.68m, we dont know the value of t, but at the same time y(t) must be 0, when the atlete reaches the ground

13. anonymous

so i have to figure out the y component first?

14. anonymous

you would have to find the value of t for which y(t)=0, you can do so setting: $y(t)=0$ but using the whole equation for y(t), and finding t from there...

15. anonymous

our unknows here are v0 and t, so we must solve the system for both of them.

16. anonymous

so the equation would be Vo(t)-1/2gt^2?

17. anonymous

1/2gt-Vsin(33.4)??

18. anonymous

t=2Vsin(33.4)/g??

19. anonymous

remember t was squared... so: $v_0 sin(33.4º)t-\frac{1}{2}gt^2 = 0$ is the first equation and $v_0cos(33.4º)t=7.68$ is the other one, in order to find v0 we need to solve the system... first can be rewritten to: $v_0sin(33.4º)t=0.5\times9.81\times t^2$ so if we take the quotient between them ( this is amethod to solve systems ) we get: $\frac{v_0sin(33.4)t}{v_0cos(33.4)t} = \frac{0.5\times 9.81 \times t^2}{7.68}$ so v0 and t cancel out in left hand side and you can get t from there, then you use that value of t in any of the original equations to find v0.