Projectile motion motorcycle jump

[nothingsus]

Homework Statement

The current world-record motorcycle jump is 77.0 m,
set by Jason Renie. Assume that he left the take-off ramp at
12.0º to the horizontal and that the take-off and landing
heights are the same. Neglecting air drag, determine his take-off
speed

Homework Equations

R = [(v0)^2/g]*sin2(theta)
5 constant acceleration equations

The Attempt at a Solution

Hi. I understand that I can use the range equation to solve this question, but I wanted to try and use the constant acceleration equations to try and understand it a little better, however I'm getting stuck.

Let u = the take off speed (magnitude of velocity vector)

u_x = ucos(12)
x_i = 0
x_f = 77
a_x = 0
t = ?

u_y = usin(12)
a = -9.8
y_i = 0
y_f = 0

I get stuck here because I don't know the time or final velocity components (not really sure how to use v_f = 0 for half the flight time either)

 

[PeroK]

Let u = the take off speed (magnitude of velocity vector)

u_x = ucos(12)
x_i = 0
x_f = 77
a_x = 0
t = ?

u_y = usin(12)
a = -9.8
y_i = 0
y_f = 0

I get stuck here because I don't know the time or final velocity components (not really sure how to use v_f = 0 for half the flight time either)

You need to think a move or two ahead. These problems don't always come out in one step. You put $t = ?$ but you should keep going with $t = \frac{x_f}{u \cos \theta}$

Now, try to find a second expression for $t$ using the vertical component. You can do it either by using the time to the maximum height (where $v_y = 0$) and symmetry of the motion. Or, you could use $s_y = u_yt + \frac{a_y t^2}{2}$ for vertical motion.

 

[nothingsus]

With your help I was able to solve it! I'll try to think further ahead for future problems.

Thanks so much!